Long range action in networks of chaotic elements

Chaotic Boltzmann machines with two elements

In this brief note, we show that chaotic Boltzmann machines truly yield samples from the probabilistic distribution of the corresponding Boltzmann machines if they are composed of only two elements. This note is an English translation (with slight modifications) of the article originally written in Japanese [H. Suzuki, Seisan Kenkyu 66 (2014), 315-316].

Topological analysis of chaotic solution of three-element memristive circuit

The simplest electronic circuit with a memristor was recently proposed. Chaotic attractors solution to this memristive circuit are topologically characterized and compared to Rossler-like attractors.

Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics

We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.

混沌几乎极小作用

Chaotic almost minimal actions

受 Furstenberg 定理启发，本文定义混沌几乎极小动力系统，分析作用群条件，并构造支持多个非原子遍历概率测度的 $\mathbb{Z}$ 与 $\mathbb{Z}^{d}$ 作用。

Chaotic behavior of group actions

In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and prove that local weak mixing implies Li-Yorke chaos if G is infinite, and positive topological entropy implies local weak mixing if G is an infinite countable discrete amenable group. Moreover, when considering a shift of finite type for actions of an infinite countable amenable group G, if the action has positive topological entropy then its homoclinic equiva…

Semiclassical matrix elements for a chaotic propagator in the Scar functions basis

A semiclassical approximation for the matrix elements of a quantum chaotic propagator in the scar function basis has been derived. The obtained expression is solely expressed in terms of canonical invariant objects. For our purpose, we have used, the recently developed, semiclassical matrix elements of the propagator in coherent states, together with the linearization of the flux in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The expression here derived is successfully verified to be exact for a (linear) cat map, after the theory is adapted to …