# TOPOLOGICAL ENTROPY AND DISTRIBUTIONAL CHAOS

## Related Articles

- A variational principle for topological pressure for certain non-compact sets. Thompson, Daniel // Journal of the London Mathematical Society;Dec2009, Vol. 80 Issue 3, p585
Let (X, d) be a compact metric space, let f:X â†¦ X be a continuous map with the specification property and let Ï•: X â†¦ â„ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form...

- TRIANGULAR MAPS NON-DECREASING ON THE FIBERS. Kocan, Zdenek // Real Analysis Exchange;2004/2005, Vol. 30 Issue 2, p519
There is a list of about 50 properties which characterize continuous maps of the interval with zero topological entropy. Most of them were proved by A. N. Sharkovsky [cf., e.g., Sharkovsky et al., Dynamics of One-Dimensional Mappings, Kluwer 1997]. It is also well known that only a few of these...

- Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space. Qiuju Xing; Yuming Shi // Abstract & Applied Analysis;2011, Special section p1
This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuousmap space, which consists of continuousmaps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of...

- Lyapunov Spectrum of Asymptotically Sub-additive Potentials. De-Jun Feng; Wen Huang // Communications in Mathematical Physics;Jul2010, Vol. 297 Issue 1, p1
For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological...

- On the relation between topological entropy and entropy dimension. Saltykov, P. S. // Mathematical Notes;Aug2009, Vol. 88 Issue 1/2, p255
For the Lipschitz mapping of a metric compact set into itself, there is a classical upper bound on topological entropy, namely, the product of the entropy dimension of the compact set by the logarithm of the Lipschitz constant. The Ghys conjecture is that, by varying the metric, one can...

- Partial weak mixing of special Topological dynamical systems. Zhang Ai-fang // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;Mar2010, Vol. 23 Issue 1, p39
The define of weakly mixing sets on special Topological dynamical systems was innestigated. Through giving the definition of Partial weak mixing proper subset, and strengthening the condition of its concept, a new concept of partial topological properly strong weak mixing is given. And an...

- On Homoclinic Tangencies in Maps with Entropy-carrying Horseshoes. Pederson, Steven M. // Nonlinear Studies;2003, Vol. 10 Issue 2, p177
Presents a study which examined sufficient conditions under which a generic interval map with non-constant topological entropy and an entropy-carrying invariant has a homoclinic tangency. Relationships between homoclinic orbits and complexity; Lemmas; Proofs.

- Topological Dynamic Classification of Antitriangular Maps. Zhiming Luo; Xianhua Tanga; Gengrong Zhang // Journal of Computational Analysis & Applications;Oct2008, Vol. 10 Issue 4, p431
We classify antitriangular maps on In by using topological dynamics. More precisely, we prove that the following properties are equivalent: (1) zero topological entropy; (2) UR(F) R(F); (3) type less than or equal to 2âˆž; and (4) AP(F) = {(x1,x2,ßª ,xn) âˆŠ In : limF2n(x1, x2,ßª , xn)...

- Families, filters and chaos. Oprocha, Piotr // Bulletin of the London Mathematical Society;Aug2010, Vol. 42 Issue 4, p713
In this paper, we use the definition of (â„±1, â„±2)-chaos introduced recently by Tan and Xiong together with the properties of residual relations as a tool in construction of various kinds of scrambled sets. In particular, we show that a continuous map acting on a compact metric space...