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A poincaré-bendixson theorem for analytic families of vector fields (1995)

Panazzolo, D. ; Roussarie, R.

Springer

Bulletin of the Brazilian Mathematical Society 26 (1995), S. 85-116

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ISSN: 1678-7714

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract We provide a characterization of the limit periodic sets for analytic families of vector fields under the hypothesis that the first jet is non-vanishing at any singular point. Also, applying the family desingularization method, we reduce the complexity of some of these sets.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01234628

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PSL(2, ℂ), the exponential and some new free groups (2018)

Panazzolo D.

Oxford University Press

In: Quarterly Journal of Mathematics

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Publikationsdatum: 2018-03-06

Beschreibung: We prove a normal form result for the groupoid of germs generated by PSL(2,ℂ) and the exponential map. We discuss three consequences of this result: (1) a generalization of a result of Cohen about the group of translations and powers, which gives a positive answer to a problem posed by Higman; (2) as proof that the subgroup of Homeo(ℝ,+∞) generated by the positive affine maps and the exponential map is isomorphic to an HNN-extension; (3) a finitary version of the immiscibility conjecture of Ecalle–Martinet–Moussu–Ramis.

Print ISSN: 0033-5606

Digitale ISSN: 1464-3847

Thema: Mathematik

Publiziert von Oxford University Press

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