Periods for transversal maps on compact manifolds with a given homology

J. Llibre, J. Paraños, J. A. Rodríguez

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)

Abstract

Let M be a compact C1 differentiable manifold such that its rational homology is Hj(M; Q) ≈ Q if j ∈ J ∪ {0}, and Hj(M; Q) ≈ {0} otherwise. Here J is a subset of the set of natural numbers N with cardinal 1, 2 or 3. 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 set of periods of f by using the Lefschetz numbers for periodic points.
Original languageEnglish
Pages (from-to)397-406
JournalHouston Journal of Mathematics
Volume24
Issue number3
Publication statusPublished - 1 Dec 1998

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