Periodic Points for Sphere Maps Preserving MonopoleFoliations

Grzegorz Graff; Michał Misiurewicz; Piotr Nowak-Przygodzki

doi:10.1007/s12346-018-0298-8

Periodic Points for Sphere Maps Preserving MonopoleFoliations

Abstract

Let S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in these classes of maps.

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artykuł w czasopiśmie wyróżnionym w JCR

Published in:

Qualitative Theory of Dynamical Systems no. 18, pages 533 - 546,
ISSN: 1575-5460

Language:

English

Publication year:

2019

Bibliographic description:

Graff G., Misiurewicz M., Nowak-Przygodzki P.: Periodic Points for Sphere Maps Preserving MonopoleFoliations// Qualitative Theory of Dynamical Systems. -Vol. 18, (2019), s.533-546

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