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  • AIP Publishing  (3)
  • 1
    Online Resource
    Online Resource
    AIP Publishing ; 2003
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 13, No. 3 ( 2003-09-01), p. 892-902
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 13, No. 3 ( 2003-09-01), p. 892-902
    Abstract: We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each end point of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an “Epistrophe Start Rule:” a new epistrophe is spawned Δ=D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2003
    detail.hit.zdb_id: 1472677-4
    SSG: 11
    Location Call Number Limitation Availability
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  • 2
    Online Resource
    Online Resource
    AIP Publishing ; 2003
    In:  Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 13, No. 3 ( 2003-09-01), p. 880-891
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 13, No. 3 ( 2003-09-01), p. 880-891
    Abstract: We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an “escape-time plot.” For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called “epistrophes,” which occur at all levels of resolution within the escape-time plot. (The word “epistrophe” comes from rhetoric and means “a repeated ending following a variable beginning.”) The epistrophes give the escape-time plot a certain self-similarity, called “epistrophic” self-similarity, which need not imply either strict or asymptotic self-similarity.
    Type of Medium: Online Resource
    ISSN: 1054-1500 , 1089-7682
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2003
    detail.hit.zdb_id: 1472677-4
    SSG: 11
    Location Call Number Limitation Availability
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  • 3
    In: Review of Scientific Instruments, AIP Publishing, Vol. 91, No. 3 ( 2020-03-01)
    Abstract: FIREBIRD-II is a National Science Foundation funded CubeSat mission designed to study the scale size and energy spectrum of relativistic electron microbursts. The mission consists of two identical 1.5 U CubeSats in a low earth polar orbit, each with two solid state detectors that differ only in the size of their geometric factors and fields of view. Having two spacecraft in close orbit allows the scale size of microbursts to be investigated through the intra-spacecraft separation when microbursts are observed simultaneously on each unit. Each detector returns high cadence (10 s of ms) measurements of the electron population from 200 keV to & gt;1 MeV across six energy channels. The energy channels were selected to fill a gap in the observations of the Heavy Ion Large Telescope instrument on the Solar, Anomalous, and Magnetospheric Particle Explorer. FIREBIRD-II has been in orbit for 5 years and continues to return high quality data. After the first month in orbit, the spacecraft had separated beyond the expected scale size of microbursts, so the focus has shifted toward conjunctions with other magnetospheric missions. FIREBIRD-II has addressed all of its primary science objectives, and its long lifetime and focus on conjunctions has enabled additional science beyond the scope of the original mission. This paper presents a brief history of the FIREBIRD mission’s science goals, followed by a description of the instrument and spacecraft. The data products are then discussed along with some caveats necessary for proper use of the data.
    Type of Medium: Online Resource
    ISSN: 0034-6748 , 1089-7623
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2020
    detail.hit.zdb_id: 209865-9
    detail.hit.zdb_id: 1472905-2
    SSG: 11
    Location Call Number Limitation Availability
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