A note on the set of periods of transversal homological sphere self-maps

Jaume Llibre

doi:https://doi.org/10.1080/1023619021000047833

A note on the set of periods of transversal homological sphere self-maps

Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

Let M be a n-dimensional manifold with the same homology than the n-dimensional sphere. A C1 map f : M → M is called transversal if for all m ∈ ℕ the graph of fm intersects transversally the diagonal of M × M at each point (x, x) such that x is a fixed point of fm. We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M.

Original language	English
Pages (from-to)	417-422
Journal	Journal of Difference Equations and Applications
Volume	9
DOIs	https://doi.org/10.1080/1023619021000047833
Publication status	Published - 1 Mar 2003

Keywords

Holomorphic maps
Homological sphere maps
Lefschetz fixed point theory
Periodic points
Set of periods
Transversal maps

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abstract = "Let M be a n-dimensional manifold with the same homology than the n-dimensional sphere. A C1 map f : M → M is called transversal if for all m ∈ ℕ the graph of fm intersects transversally the diagonal of M × M at each point (x, x) such that x is a fixed point of fm. We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M.",

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AB - Let M be a n-dimensional manifold with the same homology than the n-dimensional sphere. A C1 map f : M → M is called transversal if for all m ∈ ℕ the graph of fm intersects transversally the diagonal of M × M at each point (x, x) such that x is a fixed point of fm. We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M.

KW - Holomorphic maps

KW - Homological sphere maps

KW - Lefschetz fixed point theory

KW - Periodic points

KW - Set of periods

KW - Transversal maps

U2 - https://doi.org/10.1080/1023619021000047833

DO - https://doi.org/10.1080/1023619021000047833

M3 - Article

VL - 9

SP - 417

EP - 422

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

ER -