About 3-manifolds supporting some actions of R POT. 2and a Morses conjecture / Sobre 3-variedades suportando certas ações de R POT. 2e uma Conjectura de Morse

AUTOR(ES)
DATA DE PUBLICAÇÃO

2010

RESUMO

First we consider a family of C POT. 2actions of R POT. 2on a closed 3-manifold. One of the conditions of this family is that it admits only a finite number of singular orbits, which are all diffeomorphic to circle. For this family we will give a description of the structure of the orbits as well the 3-manifolds supporting this actions. This generalizes results of classification for locally free actions (i. e. without singularities) of R POT. 2on closed 3- manifolds obtained by Chatelet-Rosenberg-Roussarie-Weil in [12], [30] and [31]. Finally, we consider an action \phiof R POT. 2on a closed 3-manifold N which is topologically transitive (i.e. has a dense orbit in N). We will say that \phiis metrically transitive if, given any \phi-invariant compact set K, then, either K or its complement has zero measure with respect to Lebesgue measure. It is known that every action \phitopologically transitive is metrically transitive and that, in general, the reciprocal is not true. However, Morse [27] in 1946 proposed the following conjecture: any topologically transitive dynamical system with any degree of regularity is metrically transitive. The phrase "some degree of regularity" may mean, for example, that the dynamical system is real analytic, smooth, have a finite number of singularities, etc. In the second part of the thesis, we show the conjecture to the Morse for an dynamical system defined by a R POT. 2-action on a closed 3-manifold whose singular set is a finite union of orbits circle. This is a generalization of a similar result obtained by Ding in [18] for flows on closed surfaces

ASSUNTO(S)

morse s conjecture transitividade métrica conjectura de morse metric transitivity topological transitivity transitividade topológica

ACESSO AO ARTIGO

Documentos Relacionados