Related papers: Entropy for Generalized Parabolic Dynamics

Dynamics on parabolic immediate basins for rational Newton maps of entire functions have been studied. It is proved that every parabolic immediate basin contains invariant accesses to the parabolic fixed point at infinity. Moreover, among…

We develop a notion of entropy, using hyperbolic time, for laminations by hyperbolic Riemann surfaces. When the lamination is compact and transversally smooth, we show that the entropy is finite and the Poincare metric on leaves is…

In this paper, we consider certain partially hyperbolic diffeomorphisms with center of arbitrary dimension and obtain continuity properties of the topological entropy under $C^1$ perturbations. The systems considered have subexponential…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…

In this paper, we first prove that the topological entropy of induced map of any distal homeomorphism of a compact metric space is null. Then we consider induced map $2^f$ of an arbitrary pointwise periodic homeomorphism $f:X\to X$ of a…

For spacetimes that are not asymptotic to anti-de Sitter Space (non AAdS), we adapt the Lewkowycz-Maldacena procedure to find the holographic entanglement entropy. The key observation, which to our knowledge is not very well appreciated, is…

Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the…

We study genericity of dynamical properties in the space of homeomorphisms of the Cantor set and in the space of subshifts of a suitably large shift space. These rather different settings are related by a Glasner-King type correspondence:…

In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…

In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the…

Information-theoretic quantities such as Renyi entropies show a remarkable universality in their late-time behaviour across a variety of chaotic many-body systems. Understanding how such common features emerge from very different…

We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a…

This article is devoted to the study of the historic set of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms…