Related papers: Topological entropy for some isotropic cosmologica…
We consider a $C^1$ neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
I give a geometric construction of certain first order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such…
We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions…
Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…
We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole with uniform expansion. We show that under suitable…
It has been recently proposed that gravity might be an entropic force. Although a well defined fundamental description for such a mechanism is still lacking, it is still possible to address the viability of phenomenological models of…
In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the…
We study the change in topological entanglement entropy that occurs when a two-dimensional system in a topologically ordered phase undergoes a transition to another such phase due to the formation of a Bose condensate. We also consider the…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
We give an algorithm, based on the $\phi$-expansion of Parry, in order to compute the topological entropy of a class of shift spaces. The idea is the solve an inverse problem for the dynamical systems $\beta x+\alpha \mod1$.The first part…
The cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.
We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is…
In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems,…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Topological pressures of the preimages of $\epsilon$-stable sets and some certain closed subsets of stable sets in positive entropy systems are investigated. It is showed that the topological pressure of any topological system can be…
Present investigation devoted to the dynamical study of Relativistic Hydrodynamics with some thermodynamical characteristics in $f(R,G)$ gravity towards spatially homogeneous isotropic cosmological model filled with isotropic fluid. We…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln \chi (x)$ with $\chi(x)$…