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

Juan Luis García Guirao, Jaume Llibre

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5 Citations (Scopus)

Abstract

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) being x a fixed point of fm. 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. © 2013 Springer Basel.
Original languageEnglish
Pages (from-to)417-425
JournalQualitative Theory of Dynamical Systems
Volume12
Issue number2
DOIs
Publication statusPublished - 1 Oct 2013

Keywords

  • Complex projective space
  • Lefschetz number
  • Lefschetz number for periodic point
  • Lefschetz zeta function
  • Period
  • Periodic point
  • Quaternion projective space
  • Sphere
  • Transversal map

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