Dynamics of 3-Homeomorphisms with Two-Dimensional Attractors and Repellers

摘要

On closed orientable 3-manifolds, we consider a class Gdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ mathcal{G} $$end{document} of homeomorphisms such that the nonwandering set of each f ∈ Gdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ mathcal{G} $$end{document} is the finite union of surfaces such that the restriction of some power fk on each of these surfaces is a pseudo-Anosov homeomorphism. We prove that homeomorphisms of class Gdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ mathcal{G} $$end{document} exist only on 3-manifolds of the form Sg × ?/(J(z),r?1), where J : Sg → Sg is either a pseudo-Anosov homeomorphism of the surface Sg of genus g > 1 or a periodic homeomorphism commuting with some pseudo-Anosov homeomorphism. On such a manifold, we construct model homeomorphisms and find necessary and sufficient conditions for topological conjugacy of model mappings.