Se p 20 06 TOPOLOGICAL ENTROPY OF m - fold MAPS ON TREES
نویسنده
چکیده
We establish the analogue for maps on trees of the result established in [Bob02, Bob05] for interval maps, that a continuous selfmap for which all but countably many points have at least m preimages (and none have less than two) has topological entropy bounded below by logm.
منابع مشابه
Entropy Estimate for Maps on Forests
A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...
متن کامل2 5 Se p 20 06 COMPLEXITY FOR EXTENDED DYNAMICAL SYSTEMS
We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, ǫ-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same r...
متن کاملTOPOLOGICAL ENTROPY OF m-FOLD MAPS
We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a C1 map has at least m preimages then the topological entropy of the map is at least log m. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at leas...
متن کاملEntropy of a semigroup of maps from a set-valued view
In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...
متن کاملSe p 20 06 ENTROPY DISSIPATION ESTIMATES IN A ZERO – RANGE DYNAMICS
We study the exponential decay of relative entropy functionals for zero– range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of particles and the number of vertices.
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 2006