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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Periods for transversal maps via Lefschetz numbers for periodic points


Authors: A. Guillamon, X. Jarque, J. Llibre, J. Ortega and J. Torregrosa
Journal: Trans. Amer. Math. Soc. 347 (1995), 4779-4806
MSC: Primary 58F20
MathSciNet review: 1321576
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Abstract: Let $ f:M \to M$ be a $ {C^1}$ map on a $ {C^1}$ differentiable manifold. The map $ f$ is called transversal if for all $ m \in \mathbb{N}$ the graph of $ {f^m}$ intersects transversally the diagonal of $ M \times M$ at each point $ (x,x)$ such that $ x$ is a fixed point of $ {f^m}$. We study the set of periods of $ f$ by using the Lefschetz numbers for periodic points. We focus our study on transversal maps defined on compact manifolds such that their rational homology is $ {H_0} \approx \mathbb{Q}$, $ {H_1} \approx \mathbb{Q} \oplus \mathbb{Q}$ and $ {H_k} \approx \{ 0\} $ for $ k \ne 0,1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1321576-9
PII: S 0002-9947(1995)1321576-9
Keywords: Periods, transversal maps, Lefschetz numbers
Article copyright: © Copyright 1995 American Mathematical Society