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

Juan Luis García Guirao ^[1] ; Jaume Llibre
1. [1] Universidad Politécnica de Cartagena
  
  Universidad Politécnica de Cartagena
  
  Cartagena, España
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 2, 2013, págs. 417-425
Idioma: inglés
DOI: 10.1007/s12346-013-0099-z
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Resumen
- 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.