Periods for transversal maps via Lefschetz numbers for periodic points

Guillamon, A.; Jarque, X.; Llibre, J.; Ortega, J.; Torregrosa, J.

doi:10.1090/S0002-9947-1995-1321576-9

Periods for transversal maps via Lefschetz numbers for periodic points
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by A. Guillamon, X. Jarque, J. Llibre, J. Ortega and J. Torregrosa PDF

Trans. Amer. Math. Soc. 347 (1995), 4779-4806 Request permission

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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