Hyperbolic nonwandering sets without dense periodic points
نویسندگان
چکیده
منابع مشابه
Sensitive Dependence and Dense Periodic Points
We show sensitive dependence on initial conditions and dense set of periodic points imply asymptotic sensitivity, a stronger form of sensitivity , where the deviation happens not just once but infinitely many times. As a consequence it follows that all Devaney chaotic systems (e.g. logistic map) have this asymptotic sensitivity. Sensitive dependence on initial conditions (shortly, sensitivity) ...
متن کاملOn Diffeomorphisms of Compact 2-manifolds with All Nonwandering Points Periodic
The aim of the present paper is to study conditions under which all the non-wandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all dimensions, and study the remaining open question in dimension two. We present two results, one positive and one negative. The negative result: we construct a ...
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 کاملShadowing by Non Uniformly Hyperbolic Periodic Points and Uniform Hyperbolicity
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context.
متن کاملExistence of Periodic Orbits for Singular-hyperbolic Sets
It is well known that on every compact 3-manifold there is a C flow displaying a singular-hyperbolic isolated set which has no periodic orbits [BDV], [M1]. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a C flow on a compact 3manifold has a periodic orbit. 2000 Math. Subj. Class. Primary: 37D30; Secondary: 37D45.
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: Nagoya Mathematical Journal
سال: 1979
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000018456