# On the relation between topological entropy and entropy dimension

## Related Articles

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This paper adds a computational approach to a previous theoretical result illustrating how the complexity of a simple dynamical system evolves under deformations. The algorithm targets topological entropy in the 2-dimensional family P Q of compositions of two logistic maps. Estimation of the...

- Entropy and collapsing of compact complex surfaces G. P. Paternain was partially supported by CIMAT, Guanajuato, MÃ©xico. J. Petean is supported by grant 37558-E of CONACYT.. Gabriel P. Paternain; Jimmy Petean // Proceedings of the London Mathematical Society;Nov2004, Vol. 89 Issue 3, p763
We study the problem of existence of $\mathcal{F}$-structures (in the sense of Cheeger and Gromov, but not necessarily polarized) on compact complex surfaces. We give a complete classification of compact complex surfaces of KÃ¡hler type admitting $\mathcal{F}$-structures. In the...

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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...

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In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L1(Î©) + W-1,p'(Â·)(Ï‰). Moreover, we obtain the equivalence of entropy solutions and renormalized...

- Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings. Volkova, O. Yu. // Ukrainian Mathematical Journal;Nov2003, Vol. 55 Issue 11, p1733
For a special class of one-parameter families of unimodal mappings of the form ft(x): [0, 1] â†’ [0, 1], ft = atx/(x + t), 0 â‰¤ x â‰¤ 1/2, we establish that, for t âˆˆ [0, 1/(a - 2)], a > 2, the topological entropy h(ft) is a function monotonically increasing in the parameter....

- Localizing Entropies via an Open Cover. Kesong Yan; Fanping Zeng; Qi Wang // Journal of Concrete & Applicable Mathematics;Jan2008, Vol. 6 Issue 1, p209
For a given topological dynamical system (X, T), we introduce and study some entropies of open covers. The main result as follows: (1)the inequality hp(T, U) â‰¤ hm(T, U) â‰¤ htop(T, U) â‰¤ hm(T, U) + hb(T), relating pointwise pre-image entropies of open covers hp(T, U), hm(T, U),...

- On Some Topological Properties of Multigranular Rough Sets. Raghavan, R.; Tripathy, B. K. // Advances in Applied Science Research;Jun2011, Vol. 2 Issue 3, p536
Rough set theory was introduced by Pawlak [5] as a model to capture impreciseness in data and since then it has been established to be a very efficient tool for this purpose. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several...

- Pure Point Diffraction Implies Zero Entropy for Delone Sets with Uniform Cluster Frequencies. Baake, Michael; Lenz, Daniel; Richard, Christoph // Letters in Mathematical Physics;Oct2007, Vol. 82 Issue 1, p61
Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy zero if it has uniform cluster frequencies and is pure point diffractive. We also note that the patch counting entropy vanishes whenever the repetitivity...

- 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...