Related papers: Polynomial entropy of Brouwer homeomorphisms

We consider families of diffeomorphisms with dominated splittings and preserving a Borel probability measure, and we study the regularity of the Lyapunov exponents associated to the invariant bundles with respect to the parameter. We obtain…

Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…

We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…

We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk.We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium…

We introduce a new notion of local inverse metric entropy along backward trajectories for ergodic measures preserved by endomorphisms (non-invertible maps) on a compact metric space. A second notion of inverse measure entropy is defined by…

We consider entanglement entropy between two halves of space separated by a plane, in the theory of free photon in 3+1 dimensions. We show how to separate local gauge invariant quantities that belong to the two spatial regions. We calculate…

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to…

The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…

The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.

In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.

A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure.…

An orientation-preserving recurrent homeomorphism of the two-sphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

We consider variational problem related to entropy maximization in the two-dimensional Euler equations, in order to investigate the long-time dynamics of solutions with bounded vorticity. Using variations on the classical min-max principle…

In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(\Sigma_{m_-,m_+}, \sigma_\phi)$ which generalizes the standard bilateral Bernoulli shifts. The space $\Sigma_{m_-,m_+}$…

We consider an explicit example of a process, where the entropy carried by radiation through an accelerating two-plane is proportional to the decrease in the area of that two-plane even when the two-plane is not a part of any horizon of…

In this paper, we study the stability of the concentration inequality for one-dimensional complex polynomials. We provide the stability of the local concentration inequality and a global version using a Wehrl-type entropy.

A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+\alpha}$ diffeomorphism of a closed surface…