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Note: Intro -- Preface -- Acknowledgements -- Contents -- 1 A variational principle for three-dimensional steady flows of an ideal fluid -- 2 On the Riemann curvature of diffeomorphism groups -- 3 Sur la topologie des écoulements stationnaires des fluides parfaits (French) -- 4 Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid -- 5 On the topology of three-dimensional steady flows of an ideal fluid -- 6 On an a priori estimate in the theory of hydrodynamical stability -- 7 On the differential geometry of infinite-dimensional Lie groups and its applications to the hydrodynamics of perfect fluids -- 8 On a variational principle for the steady flows of perfect fluids and its applications to problems of non-linear stability -- 9 On a characteristic class arising in quantization conditions -- 10 A note on the Weierstrass preparation theorem -- 11 The stability problem and ergodic properties for classical dynamical systems -- 12 A remark on the ramification of hyperelliptic integrals as functions of parameters -- 13 Singularities of smooth mappings -- 14 Remarks on singularities of finite codimension in complex dynamical systems -- 15 Braids of algebraic functions and the cohomology of swallowtails -- 16 Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid -- 17 On the one-dimensional cohomology of the Lie algebra of divergence-free vector fields and rotation numbers of dynamical systems -- 18 The cohomology ring of the colored braid group -- 19 On cohomology classes of algebraic functions invariant under Tschirnhausen transformations -- 20 Trivial problems -- 21 Local problems of analysis -- 22 Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations. , 23 On some topological invariants of algebraic functions -- 24 Topological invariants of algebraic functions II -- 25 Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points -- 26 On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms -- 27 The topology of real algebraic curves (works of I.G. Petrovsky and their development) -- 28 On matrices depending on parameters -- 29 Lectures on bifurcations in versal families -- 30 Versal families and bifurcations of differential equations (Russian) -- 31 Remarks on the behaviour of a flow of a three-dimensional i fluid in the presence of a small perturbation of the initial vector field -- 32 The asymptotic Hopf invariant and its applications -- 33 A magnetic field in a moving conducting fluid (with Ya.B. Zeldovich, A.A.Ruzmaikin, and D.D. Sokolov) -- 34 A magnetic field in a stationary flow with stretching in a Riemannian manifold (with Ya.B. Zeldovich, A.A.Ruzmaikin, and D.D. Sokolov) -- 35 Stationary magnetic field in a periodic flow (with Ya.B. Zeldovich, A.A.Ruzmaikin, and D.D. Sokolov) -- 36 Some remarks on the antidynamo theorem -- 37 Evolution of a magnetic field under the action of transfer and diffusion -- 38 The growth of a magnetic field in a three-dimensional steady incompressible flow (with E.I.Korkina) -- 39 On evolution of a magnetic field under the action of drift and diffusion (Russian) -- 40 Exponential scattering of trajectories and its hydrodynamical applications -- 41 Kolmogorov's hydrodynamic attractors -- 42 Topological methods in hydrodynamics (with B.A. Khesin) -- 43 Translator's preface to J. Milnor's book "Morse Theory" -- 44 Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics. , 45 Comments on the paper "On a geometric theorem" by Henri Poincaré -- Acknowledgements.

Note: Intro -- Preface -- Contents -- 1 A Review of Source Models of the 2015 Illapel, Chile Earthquake and Insights from Tsunami Data -- Abstract -- 1. Introduction -- 2. Tsunami Data -- 3. Slip Distribution -- 4. Insights from Tsunami Data -- 5. Conclusions -- Acknowledgements -- REFERENCES -- 2 Rapidly Estimated Seismic Source Parameters for the 16 September 2015 Illapel, Chile Mw 8.3 Earthquake -- Abstract -- 1. Introduction -- 2. Rapid Seismic Analysis of the 2015 Mw 8.3 Earthquake -- 2.1. Point-Source Solutions -- 2.2. Back-Projection Analysis -- 2.3. Teleseismic Finite-Fault Inversion -- 2.4. Source Spectrum, Radiated Energy and Stress Drop Estimation -- 3. Discussion and Conclusion -- Acknowledgments -- REFERENCES -- 3 Rupture Process During the 2015 Illapel, Chile Earthquake: Zigzag-Along-Dip Rupture Episodes -- Abstract -- 1. Introduction -- 2. Data and Methods -- 3. Results -- 4. Discussion -- 5. Conclusion -- Acknowledgments -- REFERENCES -- 4 Imaging Rupture Process of the 2015 Mw 8.3 Illapel Earthquake Using the US Seismic Array -- Abstract -- 1. Introduction -- 2. Data and Method -- 3. Back-Projection Results -- 4. Discussions -- 5. Conclusions -- Acknowledgments -- REFERENCES -- 5 Interseismic Coupling, Megathrust Earthquakes and Seismic Swarms Along the Chilean Subduction Zone (38 -18 S) -- Abstract -- 1. Introduction -- 2. Tectonic Context -- 3. Interseismic Velocity Field -- 4. Modelling of GPS Data -- 5. Discussion -- 5.1. Kinematics of the Nazca-South America Convergence -- 5.2. The Chilean Margin is Segmented -- 5.3. Segmentation and Megathrusts -- 5.4. Interseismic Coupling and Background Seismicity -- 5.5. Creeping Low-Coupled Zones? -- 6. Conclusions -- Acknowledgments -- REFERENCES -- 6 Low-Frequency Centroid Moment Tensor Inversion of the 2015 Illapel Earthquake from Superconducting-Gravimeter Data -- Abstract. , 1. Introduction -- 2. Method -- 3. Results of Inversion -- 4. Concluding Remark -- Acknowledgments -- REFERENCES -- 7 Coseismic Fault Slip of the September 16, 2015 Mw 8.3 Illapel, Chile Earthquake Estimated from InSAR Data -- Abstract -- 1. Introduction -- 2. SAR Data and InSAR Processing -- 3. Fault Slip Modeling -- 4. Discussion -- 5. Conclusions -- Acknowledgments -- REFERENCES -- 8 Analysis of the Illapel Mw = 8.3 Thrust Earthquake Rupture Zone Using GOCE-Derived Gradients -- Abstract -- 1. Introduction -- 2. Oceanic Features and Seismic Segmentation -- 3. Methodology -- 4. Results -- 5. Discussion -- 5.1. Oceanic features controlling rupture propagation -- 6. Concluding Remarks -- Acknowledgments -- Appendix 1: The Maule 2010 and Iquique 2014 Earthquakes -- Appendix 2: Preliminary Slip Models -- Appendix 3: GOCE Error Assessment -- Appendix 4: Uncertainties Which Should Originate from the Topography and Sediment Corrections -- Appendix 5 -- REFERENCES -- 9 Chile2015: Le´vy Flight and Long-Range Correlation Analysis of Earthquake Magnitudes in Chile -- Abstract -- 1. Introduction -- 2. Tectonic Settings -- 3. Truncated Le´vy Flight Model -- 4. Detrended Fluctuation Analysis, DFA -- 5. Results and Discussion -- 6. Conclusions -- Acknowledgments -- REFERENCES -- 10 Time-Based Network Analysis Before and After the Mw 8.3 Illapel Earthquake 2015 Chile -- Abstract -- 1. Introduction -- 2. Data and Network Analysis -- 2.1. Maximum Likelihood Estimation and Linear Regression -- 3. Variability of the Complex Networks -- 4. Discussion -- 5. Concluding Remarks -- Acknowledgments -- REFERENCES -- 11 Chilean Earthquakes: Aquifer Responses at the Russian Platform -- Abstract -- 1. Introduction -- 2. Observational Data and Research Methods -- 3. Measurement Results -- 4. Discussion -- 5. Conclusions -- Acknowledgments -- REFERENCES. , 12 Ionospheric Plasma Response to Mw 8.3 Chile Illapel Earthquake on September 16, 2015 -- Abstract -- 1. Introduction -- 2. Seismo-Tectonics of Chile Subduction Zone -- 2.1. Mw 8.3 Illapel Earthquake -- 2.2. Vertical Deformation of Illapel Earthquake -- 3. GPS Data Analysis -- 4. Results and Discussion -- 5. Conclusions -- Acknowledgments -- REFERENCES -- 13 Remote Sensing of Atmospheric and Ionospheric Signals Prior to the Mw 8.3 Illapel Earthquake, Chile 2015 -- Abstract -- 1. Introduction -- 2. Materials and Methods -- 2.1. Study Area -- 2.2. Data Preparation -- 3. Results and Discussion -- 3.1. Anomalous Atmospheric and Ionospheric Phenomena -- 3.2. Cause for the Pre-Earthquake Anomalies within the Solid Earth -- 4. Conclusion -- Acknowledgments -- REFERENCES -- 14 Chile2015: Induced Magnetic Fields on the Z Component by Tsunami Wave Propagation -- Abstract -- 1. Introduction -- 2. Data and Methodology -- 3. Results and analyses -- 4. Conclusions -- Acknowledgments -- REFERENCES -- 15 First Report on Seismogenic Magnetic Disturbances over Brazilian Sector -- Abstract -- 1. Introduction -- 2. Datasets -- 3. Seismometer and Magnetometer Measurements over Brazil -- 4. Discussion -- 5. Conclusion -- Acknowledgements -- REFERENCES -- 16 The 16 September 2015 Chile Tsunami from the Post-Tsunami Survey and Numerical Modeling Perspectives -- Abstract -- 1. Introduction -- 2. Bathymetry and Coastal Morphology -- 3. Tide Gages Data Analysis -- 4. Post Tsunami Survey -- 5. Numerical Simulation -- 6. Discussion -- 7. Conclusions -- Acknowledgments -- REFERENCES -- 17 Field Survey of the 2015 Chile Tsunami with Emphasis on Coastal Wetland and Conservation Areas -- Abstract -- 1. Introduction -- 2. Post Tsunami Field Survey -- 3. Site Specific Surveys -- 3.1. El Yali National Reserve -- 3.2. Santo Domingo to Quintay -- 3.3. Valpara ´so and Conco´n bays. , 3.4. Quintero to Pichidangui -- 3.5. Los Vilos to Playa Amarilla -- 3.6. Chigualoco to La Cebada -- 3.7. Punta Lengua de Vaca a Totoralillo -- 3.8. La Herradura, Coquimbo to Punta Teatinos -- 3.9. Caleta Los Hornos to Chungungo -- 4. Conclusions -- Acknowledgments -- Appendix -- REFERENCES -- 18 A Study of the 2015 Mw 8.3 Illapel Earthquake and Tsunami: Numerical and AnalyticalApproaches -- Abstract -- 1. Introduction -- 1.1. Previous studies -- 2. Slip Distribution Solution -- 2.1. USGS Solution -- 2.2. Berkeley Solution -- 3. Tsunami Modeling -- 3.1. Numerical Modeling and Setup -- 3.2. Analytical Modeling -- 3.3. Field Observations -- 4. Tsunami Run-up Inversion -- 5. Results -- 6. Discussion and Conclusions -- Acknowledgments -- REFERENCES -- 19 Real-Time Assessment of the 16 September 2015 Chile Tsunami and Implications for Near-Field Forecast -- Abstract -- 1. Introduction -- 2. Tsunami Forecast Method -- 3. Assessment of Tsunami Source and Energy in Real Time -- 4. Coastal Impacts and Model Accuracy -- 5. Implications for Fast and Reliable Forecast Application in the Near Field -- 6. Conclusion and Future Work -- Acknowledgments -- REFERENCES -- 20 Comparison Between Tsunami Signals Generated by Different Source Models and the Observed Data of the Illapel 2015 Earthquake -- Abstract -- 1. Introduction -- 2. Tsunami Modeling -- 3. Grid Generation -- 4. Tsunami Signals -- 4.1. Observed Data -- 4.2. Fault Models -- 5. Results -- 6. Discussion -- 7. Conclusions -- Acknowledgments -- REFERENCES -- 21 Tsunami Characteristics Along the Peru-Chile Trench: Analysis of the 2015 Mw8.3 Illapel, the 2014 Mw8.2 Iquique and the 2010 Mw8.8 Maule Tsunamis in the Near-field -- Abstract -- 1. Introduction -- 2. The Three Recent Chilean Tsunamis -- 3. Results -- 3.1. Analysis of the Co-seismic Deformation -- 3.2. Tsunami Generation and Propagation. , 3.3. Tsunami Signal -- 4. Discussion -- 4.1. The Relative Effect of the Onshore Co-seismic Deformation -- 4.2. Continental Margin Controlling the Tsunami Behavior -- 5. Conclusions -- Acknowledgments -- REFERENCES -- 22 Tsunami Penetration in Tidal Rivers, with Observations of the Chile 2015 Tsunami in Rivers in Japan -- Abstract -- 1. Introduction -- 2. Study Area -- 3. Preliminary Analysis of the Observations -- 4. Admittance Computations -- 4.1. Cross-Examination of Computed Admittances -- 5. Physics Behind Wave-Locked Slope -- 5.1. Governing Equations -- 5.2. WLS in a Purely Incident Wave -- 5.3. Flow Estimates with WLS -- 5.4. Tidal Wave-Locked Slope and Friction UponTsunami -- 6. Conclusions -- Acknowledgments -- REFERENCES.

Note: Intro -- Title Page -- Copyright Page -- Preface -- THE NINTH EDITION -- THE TEACHING AND LEARNING PACKAGE -- ACKNOWLEDGMENTS -- About the Authors -- Dedication -- CHAPTER 1 - Introduction to Human Geography -- WHAT IS HUMAN GEOGRAPHY? -- WHAT ARE GEOGRAPHIC QUESTIONS? -- WHY DO GEOGRAPHERS USE MAPS, AND WHAT DO MAPS TELL US? -- WHY ARE GEOGRAPHERS CONCERNED WITH SCALE AND CONNECTEDNESS? -- WHAT ARE GEOGRAPHIC CONCEPTS, AND HOW ARE THEY USED IN ANSWERING GEOGRAPHIC QUESTIONS? -- CHAPTER 2 - Population -- WHERE IN THE WORLD DO PEOPLE LIVE AND WHY? -- WHY DO POPULATIONS RISE OR FALL IN PARTICULAR PLACES? -- WHY DOES POPULATION COMPOSITION MATTER? -- HOW DOES THE GEOGRAPHY OF HEALTH INFLUENCE POPULATION DYNAMICS? -- HOW DO GOVERNMENTS AFFECT POPULATION CHANGE? -- CHAPTER 3 - Migration -- WHAT IS MIGRATION? -- WHY DO PEOPLE MIGRATE? -- WHERE DO PEOPLE MIGRATE? -- HOW DO GOVERNMENTS AFFECT MIGRATION? -- CHAPTER 4 - Local Culture, Popular Culture, and Cultural Landscapes -- WHAT ARE LOCAL AND POPULAR CULTURES? -- HOW ARE LOCAL CULTURES SUSTAINED? -- HOW IS POPULAR CULTURE DIFFUSED? -- HOW CAN LOCAL AND POPULAR CULTURES BE SEEN IN THE CULTURAL LANDSCAPE? -- CHAPTER 5 - Identity: Race, Ethnicity, Gender, and Sexuality -- WHAT IS IDENTITY, AND HOW ARE IDENTITIES CONSTRUCTED? -- HOW DO PLACES AFFECT IDENTITY, AND HOW CAN WE SEE IDENTITIES IN PLACES? -- HOW DOES GEOGRAPHY REFLECT AND SHAPE POWER RELATIONSHIPS AMONG GROUPS OF PEOPLE? -- CHAPTER 6 - Language -- WHAT ARE LANGUAGES, AND WHAT ROLE DO LANGUAGES PLAY IN CULTURES? -- WHY ARE LANGUAGES DISTRIBUTED THE WAY THEY ARE? -- HOW DO LANGUAGES DIFFUSE? -- WHAT ROLE DOES LANGUAGE PLAY IN MAKING PLACES? -- CHAPTER 7 - Religion -- WHAT IS RELIGION, AND WHAT ROLE DOES IT PLAY IN CULTURE? -- WHERE DID THE MAJOR RELIGIONS OF THE WORLD ORIGINATE, AND HOW DO RELIGIONS DIFFUSE?. , HOW IS RELIGION SEEN IN THE CULTURAL LANDSCAPE? -- WHAT ROLE DOES RELIGION PLAY IN POLITICAL CONFLICTS? -- CHAPTER 8 - Political Geography -- HOW IS SPACE POLITICALLY ORGANIZED INTO STATES AND NATIONS? -- HOW DO STATES SPATIALLY ORGANIZE THEIR GOVERNMENTS? -- HOW ARE BOUNDARIES ESTABLISHED, AND WHY DO BOUNDARY DISPUTES OCCUR? -- HOW DO GEOPOLITICS AND CRITICAL GEOPOLITICS HELP US UNDERSTAND THE WORLD? -- WHAT ARE SUPRANATIONAL ORGANIZATIONS, AND WHAT IS THE FUTURE OF THE STATE? -- CHAPTER 9 - Urban Geography -- WHEN AND WHY DID PEOPLE START LIVING IN CITIES? -- WHERE ARE CITIES LOCATED AND WHY? -- HOW ARE CITIES ORGANIZED, AND HOW DO THEY FUNCTION? -- HOW DO PEOPLE MAKE CITIES? -- WHAT ROLE DO CITIES PLAY IN GLOBALIZATION? -- CHAPTER 10 - Development -- HOW DO YOU DEFINE AND MEASURE DEVELOPMENT? -- HOW DOES GEOGRAPHICAL SITUATION AFFECT DEVELOPMENT? -- WHAT ARE THE BARRIERS TO AND THE COSTS OF ECONOMIC DEVELOPMENT? -- HOW DO POLITICAL AND ECONOMIC INSTITUTIONS INFLUENCE UNEVEN DEVELOPMENT WITHIN STATES? -- CHAPTER 11 - Agriculture -- WHAT IS AGRICULTURE, AND WHERE DID AGRICULTURE BEGIN? -- HOW DID AGRICULTURE CHANGE WITH INDUSTRIALIZATION? -- WHAT IMPRINT DOES AGRICULTURE MAKE ON THE CULTURAL LANDSCAPE? -- WHAT IS THE GLOBAL PATTERN OF AGRICULTURE AND AGRIBUSINESS? -- CHAPTER 12 - Industry and Services -- WHERE DID THE INDUSTRIAL REVOLUTION BEGIN, AND HOW DID IT DIFFUSE? -- HOW DO LOCATION THEORIES EXPLAIN INDUSTRIAL LOCATION? -- HOW HAS INDUSTRIAL PRODUCTION CHANGED? -- WHERE ARE THE MAJOR INDUSTRIAL BELTS IN THE WORLD TODAY AND WHY? -- WHAT IS THE SERVICE ECONOMY, AND WHERE ARE SERVICES CONCENTRATED? -- CHAPTER 13 - Human Environment -- HOW HAS THE EARTH ENVIRONMENT CHANGED OVER TIME? -- HOW HAVE HUMANS IMPACTED EARTH'S ENVIRONMENT? -- WHAT ARE THE MAJOR FACTORS CONTRIBUTING TO ENVIRONMENTAL CHANGE TODAY?. , HOW ARE HUMANS RESPONDING TO ENVIRONMENTAL CHANGE? -- CHAPTER 14 - Globalization and the Geography of Networks -- WHAT IS GLOBALIZATION, AND WHAT ROLE DO NETWORKS PLAY IN GLOBALIZATION? -- AT WHAT SCALES DO NETWORKS OPERATE IN THE GLOBALIZED WORLD? -- HOW HAVE IDENTITIES CHANGED IN A GLOBALIZED WORLD? -- APPENDIX A - Maps -- APPENDIX B - Area and Demographic Data for the World's States -- APPENDIX C -- APPENDIX D -- Index.

Note: Intro -- The Authors' Preface -- Contents -- 1 Nonlinear Oscillations -- 1.1 Nonlinear Oscillations of a Conservative Single-Degree-of-Freedom System -- 1.1.1 Qualitative Description of Motion by the Phase Plane Method -- 1.2 Oscillations of a Mathematical Pendulum. Elliptic Functions -- 1.3 Small-Amplitude Oscillations of a Conservative Single-Degree-of-Freedom System -- 1.3.1 Straightforward Expansion -- 1.3.2 The Method of Multiple Scales -- 1.3.3 The Method of Averaging: The Van der Pol Equation -- 1.3.4 The Generalized Method of Averaging. The Krylov- Bogolyubov Approach -- 1.4 Forced Oscillations of an Anharmonic Oscillator -- 1.4.1 Straightforward Expansion -- 1.4.2 A Secondary Resonance at 9 ˜ ±3 -- 1.4.3 A Primary Resonance: Amplitude-Frequency Response -- 1.5 Self-Oscillations: Limit Cycles -- 1.5.1 An Analytical Solution of the Van der Pol Equation for Small Nonlinearity Parameter Values -- 1.5.2 An approximate solution of the Van der Pol equation for large nonlinearity parameter values -- 1.6 External Synchronization of Self-Oscillating Systems -- 1.7 Parametric Resonance -- 1.7.1 The Floquet Theory -- 1.7.2 An Analytical Solution of the Mathieu Equation for Small Nonlinearity Parameter Values -- 2 IntegrableSystems -- 2.1 Equations of Motion for a Rigid Body -- 2.1.1 Euler's Angles -- 2.1.2 Euler's Kinematic Equations -- 2.1.3 Moment of Inertia of a Rigid Body -- 2.1.4 Euler's Dynamic Equations -- 2.1.5 S.V. Kovalevskaya's Algorithm for Integrating Equations of Motion for a Rigid Body about a Fixed Point -- 2.2 The Painlevé Property for Differential Equations -- 2.2.1 A Brief Overview of the Analytic Theory of Differential Equations -- 2.2.2 A Modern Algorithm of Analysis of Integrable Systems -- 2.2.3 Integrability of the Generalized Henon-Heiles Model. , 2.2.4 The Linearization Method for Constructing Particular Solutions of a Nonlinear Model -- 2.3 Dynamics of Particles in the Toda Lattice: Integration by the Method of the Inverse Scattering Problem -- 2.3.1 Lax's Representation -- 2.3.2 The Direct Scattering Problem -- 2.3.3 The inverse scattering transform -- 2.3.4 N-Soliton Solutions -- 2.3.5 The Inverse Scattering Problem and the Riemann Problem -- 2.3.6 Solitons as Elementary Excitations of Nonlinear Integrable Systems -- 2.3.7 The Darboux-Backlund Transformations -- 2.3.8 Multiplication of Integrable Equations: The modified Toda Lattice -- 3 Stability of Motion and Structural Stability -- 3.1 Stability of Motion -- 3.1.1 Stability of Fixed Points and Trajectories -- 3.1.2 Succession Mapping or the Poincare Map -- 3.1.3 Theorem about the Volume of a Phase Drop -- 3.1.4 Poincare-Bendixson Theorem and Topology of the Phase Plane -- 3.1.5 The Lyapunov Exponents -- 3.2 Structural Stability -- 3.2.1 Topological Reconstruction of the Phase Portrait -- 3.2.2 Coarse Systems -- 3.2.3 Cusp Catastrophe -- 3.2.4 Catastrophe Theory -- 4 Chaos in Conservative Systems -- 4.1 Determinism and Irreversibility -- 4.2 Simple Models with Unstable Dynamics -- 4.2.1 Homoclinic Structure -- 4.2.2 The Anosov Map -- 4.2.3 The Tent Map -- 4.2.4 The Bernoulli Shift -- 4.3 Dynamics of Hamiltonian Systems Close to Integrable -- 4.3.1 Perturbed Motion and Nonlinear Resonance -- 4.3.2 The Zaslavsky-Chirikov Map -- 4.3.3 Chaos and Kolmogorov-Arnold-Moser Theory -- 5 Chaos and Fractal Attractors in Dissipative Systems -- 5.1 On the Nature of Turbulence -- 5.2 Dynamics of the Lorenz Model -- 5.2.1 Dissipativity of the Lorenz Model -- 5.2.2 Boundedness of the Region of Stationary Motion -- 5.2.3 Stationary Points -- 5.2.4 The Lorenz Model's Dynamic Regimes as a Result of Bifurcations -- 5.2.5 Motion on a Strange Attractor. , 5.2.6 Hypothesis About the Structure of a Strange Attractor -- 5.2.7 The Lorenz Model and the Tent Map -- 5.2.8 Lyapunov Exponents -- 5.3 Elements of Cantor Set Theory -- 5.3.1 Potential and Actual Infinity -- 5.3.2 Cantor's Theorem and Cardinal Numbers -- 5.3.3 Cantor sets -- 5.4 Cantor Structure of Attractors in Two-Dimensional Mappings -- 5.4.1 The Henon Map -- 5.4.2 The Ikeda Map -- 5.4.3 An Analytical Theory of the Cantor Structure of Attractors -- 5.5 Mathematical Models of Fractal Structures -- 5.5.1 Massive Cantor Set -- 5.5.2 A binomial multiplicative process -- 5.5.3 The Spectrum of Fractal Dimensions -- 5.5.4 The Lyapunov Dimension -- 5.5.5 A Relationship Between the Mass Exponent and the Spectral Function -- 5.5.6 The Mass Exponent of the Multiplicative Binomial Process -- 5.5.7 A Multiplicative Binomial Process on a Fractal Carrier -- 5.5.8 A Temporal Data Sequence as a Source of Information About an Attractor -- 5.6 Universality and Scaling in the Dynamics of One-Dimensional Maps -- 5.6.1 General Regularities of a Period-Doubling Process -- 5.6.2 The Feigenbaum-Cvitanovic Equation -- 5.6.3 A Universal Regularity in the Arrangement of Cycles: AUniversal Power Spectrum -- 5.7 Synchronization of Chaotic Oscillations -- 5.7.1 Synchronization in a System of Two Coupled Maps -- 5.7.2 Types and Criteria of Synchronization -- Conclusion -- References -- Index.