On the Dynamics of Homology-preserving Homeomorphisms of the Annulus
نویسنده
چکیده
We consider the homeomorphisms of the compact annulus A = S1 × [−1, 1] isotopic to the symmetry SA which interchanges the two boundary components. We prove that if such a homeomorphism is, in some sense, conservative and twisted, then it possesses a periodic orbit of period exactly two. This can be regarded as a counterpart of the Poincaré-Birkhoff theorem in the isotopy class of SA.
منابع مشابه
Periodic Point Free Homeomorphisms of the Open Annulus: from Skew Products to Non-fibred Maps
The aim of this paper is to study and compare the dynamics of two classes of periodic point free homeomorphisms of the open annulus, homotopic to the identity. First, we consider skew products over irrational rotations (often called quasiperiodically forced monotone maps) and derive a decomposition of the phase space that strengthens a classification given by J. Stark. There exists a sequence o...
متن کاملBounded homeomorphisms of the open annulus
We prove a generalization of the Poincaré-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the study of bounded homeomorphisms of the open annulus. We prove a fixed point theorem for bounded homeomorphisms and study the special case of those homeomorphis...
متن کاملChain Transitivity and Rotation Shadowing for Annulus Homeomorphisms
We present a relation between the rotation of chain transitive sets and the rotation shadowing for annulus homeomorphisms isotopic to identity.
متن کاملRealisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss re...
متن کاملCombining persistent homology and invariance groups for shape comparison
In many applications concerning the comparison of data expressed by R-valued functions defined on a topological space X, the invariance with respect to a given group G of self-homeomorphisms of X is required. While persistent homology is quite efficient in the topological and qualitative comparison of this kind of data when the invariance group G is the group Homeo(X) of all selfhomeomorphisms ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008