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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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Details

Category:
Articles
Type:
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
DOI:
Digital Object Identifier (open in new tab) 10.1007/s12346-018-0298-8
Sources of funding:
Verified by:
Gdańsk University of Technology

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