A chaotic function with zero topological entropy having a non-perfect attractor
A classification of braid types for periodic orbits of diffeomorphisms of surfaces of genus one with topological entropy zero.
We classify the braid types that can occur for finite unions of periodic orbits of diffeomorphisms of surfaces of genus one with zero topological entropy.
A Remark on the Topological Entropy of Homeomorphisms.
Absolutely continuous measures for certain maps of an interval
Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.
The Lefschetz zeta function associated to a continuous self-map f of a compact manifold is a rational function P/Q. According to the parity of the degrees of the polynomials P and Q, we analyze when the set of periodic points of f is infinite and when the topological entropy is positive.
An invariant for continuous mappings
Approximation of the Steady State System State Distribution of the M/G/1 Retrial Queue With Impatient Customers
Bifurcations in One Dimension. I. The Nonwandering Set.
Commutativity and non-commutativity of topological sequence entropy
In this paper we study the commutativity property for topological sequence entropy. We prove that if is a compact metric space and are continuous maps then for every increasing sequence if , and construct a counterexample for the general case. In the interim, we also show that the equality is true if but does not necessarily hold if is an arbitrary compact metric space.
Comparing measure theoretic entropy for -finite measures with topological entropy
Completion theorem for uniform entropy
Modifying Bowen's entropy, we introduce a new uniform entropy. We prove that the completion theorem for uniform entropy holds in the class of all metric spaces. However, the completion theorem for Bowen's entropy does not hold in the class of all totally bounded metric spaces.
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Die Entropie einer linear gebrochenen Funktion.
Eine Bemerkung zur topologischen Entropie.
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...
Entropic approximation in kinetic theory
Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular...
Entropie de l'image inverse d'une application
Entropie et itinéraires des applications unimodales de l'intervalle
Entropies of self-mappings of topological spaces with richer structures
For mappings , where is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the -entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of , which is closely connected with the -entropy of .
Entropy, capacity and arrangements on the cube.