Periodic structure of transversal maps on CP^n, HP^n and S^p S^q

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 pr...

Descripción completa

Detalles Bibliográficos
Autores: Guirao, Juan Luis Garcia|||0000-0003-2788-809X, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150655
Acceso en línea:https://ddd.uab.cat/record/150655
https://dx.doi.org/urn:doi:10.1007/s12346-013-0099-z
Access Level:acceso abierto
Palabra clave:Periodic point
Period
Transversal map
Lefschetz zeta function
Lefschetz number
Lefschetz number for periodic point
Sphere
Complex projective space
Quaternion projective space
Descripción
Sumario: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 6= 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.