Related papers: Positive topological entropy implies chaos DC2

Topological defects are ubiquitous from solid state physics to cosmology, where they drive phase transitions by proliferating as domain walls, monopoles or vortices. As quantum excitations, they often display fractional charge and anyonic…

We study anomalous hydrodynamics with a dyonic charge. We show that the local second law of thermodynamics constrains the structure of the anomaly in addition to the structure of the hydrodynamic constitutive equations. In particular, we…

We consider classical two-dimensional Kepler system with spin-orbit coupling and show that at a sufficiently strong coupling it demonstrates a chaotic behavior. The chaos emerges since the spin-orbit coupling reduces the number of the…

A universal theory of chaos is presented which postulates the self-organized ordered growth of self-similar, scale invariant, eddy energy structures by space-time integration of inherent microscale energy generation mechanisms in the medium…

The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…

Let $f_{i},i=1,2$ be continuous bundle random dynamical systems over an ergodic compact metric system $(\Omega,\mathcal{F},\mathbb{P},\vartheta)$. Assume that ${\bf a}=(a_{1},a_{2})\in\mathbb{R}^{2}$ with $a_{1}>0$ and $a_{2}\geq0$, $f_{2}$…

We consider a natural Hamiltonian system with two degrees of freedom and Hamiltonian $H=\|p\|^2/2+V(q)$. The configuration space $M$ is a closed surface (for noncompact $M$ certain conditions at infinity are required). It is well known that…

Using standard definitions of chaos (as positive Kolmogorov-Sinai entropy) and diffusion (that multiple time distribution functions are Gaussian), we show numerically that both chaotic and nonchaotic systems exhibit diffusion, and hence…

We introduce a theory for the stability of a condensate in an optical lattice. We show that the understanding of the stability-to-ergodicity transition involves the fusion of monodromy and chaos theory. Specifically, the condensate can…

We disprove the conjecture that distributional chaos of type 3 (briefly, DC3) is iteration invariant and show that a slightly strengthened definition, denoted by DC2$\frac{1}{2}$, is preserved under iteration, i.e. $f^n$ is DC2$\frac{1}{2}$…

We prove that all entire transcendental entire functions have infinite topological entropy.

This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…

We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of…

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…

We give a general review on the application of Ergodic theory to the investigation of dynamics of the Yang-Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In…

The objective of this paper is to characterize the structure of the set $\Theta$ for a continuous ergodic upper probability $\mathbb{V}=\sup_{P\in\Theta}P$ (Theorem \ref {main result}): . $\Theta$ contains a finite number of ergodic…

We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

Bohr chaoticity is a topological notion of dynamical complexity defined through non-orthogonality to all non-trivial weights. It is strictly stronger than positivity of topological entropy and also has strong consequences for the…