Related papers: Rescaled topological entropy
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space…
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…
Topological phases are unique states of matter which support non-local excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement…
In this paper, we study the regularity of topological entropy, as a function on the space of Riemannian metrics endowed with the $C^0$ topology. We establish several instances of entropy robustness (persistence of entropy non-vanishing…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…
In this paper, we prove that for any given closed contact manifold, there exists an infinite-dimensional space of Riemannian metrics which can be identified with the space of bundle metrics on the induced contact distribution. For each such…
We obtain upper estimates for the bottom (that is, greatest lower bound) of the essential spectrum of weighted Laplacian operator of a weighted manifold under assumptions of the volume growth of their geodesic balls and spheres.…
Let $\mathbb{K}$ be a discrete field and $(V, \phi)$ a flow over the category of locally linearly compact $\mathbb{K}$-spaces. Here we give the formulas to compute the topological entropy of $(V,\phi)$ subject to the extension or the…
In this paper, we have studied 'absorbing' and 'balanced' sets in an Exponential Vector Space (\emph{evs} in short) over the field $\mathbb K$ of real or complex. These sets play pivotal role to describe several aspects of a topological…
In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume…
For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold $M$, and more generally of a finite simplicial complex $X$, vanishes or is positive. These topological conditions are expressed in…
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives…
We prove existence of maximal entropy measures for an open set of non-uniformly expanding local diffeomorphisms on a compact Riemannian manifold. In this context the topological entropy coincides with the logarithm of the degree, and these…
An anisotropic surface energy is the integral of an energy density that depends on the normal at each point over the considered surface, and it is a generalization of surface area. The minimizer of such an energy among all closed surfaces…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
Quantum ergodicity asserts that almost all infinite sequences of eigenstates of a quantized ergodic system are equidistributed in the phase space. On the other hand, there are might exist exceptional sequences which converge to different…
A positive contactomorphism of a contact manifold $M$ is the end point of a contact isotopy on $M$ that is always positively transverse to the contact structure. Assume that $M$ contains a Legendrian sphere $\Lambda$, and that $(M,\Lambda)$…
An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…