Registro completo |
Provedor de dados: |
Anais da ABC (AABC)
|
País: |
Brazil
|
Título: |
About periodic and quasi-periodic orbits of a new type for twist maps of the torus
|
Autores: |
ADDAS-ZANATA,SALVADOR
|
Data: |
2002-03-01
|
Ano: |
2002
|
Palavras-chave: |
Twist maps
Rotational invariant circles
Topological methods
Vertical rotation number
Nielsen-Thurston theory
|
Resumo: |
We prove that for a large and important class of C¹ twist maps of the torus periodic and quasi-periodic orbits of a new type exist, provided that there are no rotational invariant circles (R.I.C's). These orbits have a non-zero "vertical rotation number'' (V.R.N.), in contrast to what happens to Birkhoff periodic orbits and Aubry-Mather sets. The V.R.N. is rational for a periodic orbit and irrational for a quasi-periodic. We also prove that the existence of an orbit with a V.R.N = a > 0, implies the existence of orbits with V.R.N = b, for all 0 < b < a. And as a consequence of the previous results we get that a twist map of the torus with no R.I.C's has positive topological entropy, which is a very classical result. In the end of the paper we present some applications and examples, like the Standard map, such that our results apply.
|
Tipo: |
Info:eu-repo/semantics/article
|
Idioma: |
Inglês
|
Identificador: |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000100003
|
Editor: |
Academia Brasileira de Ciências
|
Relação: |
10.1590/S0001-37652002000100003
|
Formato: |
text/html
|
Fonte: |
Anais da Academia Brasileira de Ciências v.74 n.1 2002
|
Direitos: |
info:eu-repo/semantics/openAccess
|