Periodic points of surface homeomorphisms with zero entropy
نویسندگان
چکیده
منابع مشابه
Surface Homeomorphisms with Zero Dimensional Singular Set
We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set Σ(f) is totally disconnected, then f is topologically conjugate to a conformal transformation.
متن کاملHomeomorphisms of the Circle without Periodic Points!
Homeomorphisms of the circle were first considered by Poincare* who used them to obtain qualitative results for a class of differential equations on the torus. He classified those which have a dense orbit by showing that they are topologically equivalent to a rotation through an angle incommensurable with IT. However, Denjoy showed that there exist homeomorphisms of the circle without periodic ...
متن کاملThe Rotation Set and Periodic Points for Torus Homeomorphisms
We consider the rotation set ρ(F ) for a lift F of an area preserving homeomorphism f : T → T, which is homotopic to the identity. The relationship between this set and the existence of periodic points for f is least well understood in the case when this set is a line segment. We show that in this case if a vector v lies in ρ(F ) and has both co-ordinates rational, then there is a periodic poin...
متن کاملDirectional Uniformities , Periodic Points , and Entropy
Dynamical systems generated by d > 2 commuting homeomorphisms (topological Zd-actions) contain within them structures on many scales, and in particular contain many actions of Zk for 1 6 k 6 d. Familiar dynamical invariants for homeomorphisms, like entropy and periodic point data, become more complex and permit multiple definitions. We briefly survey some of these and other related invariants i...
متن کاملPowers of Homeomorphisms with Almost Periodic Properties
Let X be a topological space (an "accessible space," a "1-space," or a " TV-space " in the terminology of Fréchet, Kuratowski, or Alexandroff-Hopf, respectively) and let f(X) = X be a homeomorphism. We use the following terminology, which was suggested by G. A. Hedlund and which is to be carefully distinguished from those terminologies used by Birkhoff, Ayres, Whyburn, and others. A point x of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1983
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s014338570000198x