Periodic Structure of Transversal Maps on CPn, HPn and Sp × Sq

  1. Juan Luis García Guirao 1
  2. Jaume Llibre
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2013

Volume: 12

Issue: 2

Pages: 417-425

Type: Article

DOI: 10.1007/S12346-013-0099-Z DIALNET GOOGLE SCHOLAR

More publications in: Qualitative theory of dynamical systems

Abstract

A C1 map f : M → M is called transversal if for all m ∈ N the graph of f m intersects transversally the diagonal of M × M at each point (x, x) being x a fixed point of f m. Let CPn be the n-dimensional complex projective space, HPn be the n-dimensional quaternion projective space and Sp ×Sq be the product space of the p-dimensional with the q-dimensional spheres, p = q. Then for the cases M equal to CPn, HPn and Sp × Sq we study the set of periods of f by using the Lefschetz numbers for periodic points.

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Funding information

Acknowledgments The first author was partially supported by MICIIN/FEDER grant number MTM2008-03679/MTM, Fundación Séneca de la Región de Murcia, grant number 08667/PI/08 and Junta de Comu-nidades de Castilla-La Mancha, grant number PEII09-0220-0222. The second author was partially supported by MICIIN/FEDER grant number MTM2008-03437, an AGAUR grant number 2009SGR-410, ICREA Academia and FP7-PEOPLE-2012-IRSES-316338.

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