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Related papers: Periodic orbit quantization of chaotic maps by har…

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In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…

Dynamical Systems · Mathematics 2007-05-23 Artur Avila , Carlos Gustavo Moreira

Analysis of the PPF chaos control method used in biological experiments shows that it can robustly control a wider class of systems than previously believed, including those without stable manifolds. This can be exploited to find the…

Chaotic Dynamics · Physics 2007-05-23 Daniel T. Kaplan

Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…

Adaptation and Self-Organizing Systems · Physics 2015-03-17 Christian Bick , Christoph Kolodziejski , Marc Timme

We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a…

Mathematical Physics · Physics 2022-02-09 Ivan Dynnikov , Andrei Maltsev

An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…

Chaotic Dynamics · Physics 2019-07-16 Gabriel M. Lando , Alfredo M. Ozorio de Almeida

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…

Chaotic Dynamics · Physics 2009-11-07 Tsampikos Kottos , Uzy Smilansky

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

Mathematical Physics · Physics 2009-11-10 Michel Vittot

A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 Oded Agam

We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling…

Quantum Physics · Physics 2007-05-23 H. Kröger

Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…

Instrumentation and Methods for Astrophysics · Physics 2017-01-26 Yanning Fu , Jacques Laskar

A numerical and experimental study of a control method aimed at channeling chaos by building barriers in phase space is performed on a paradigm for wave-particle interaction, i.e., a traveling wave tube. Control of chaotic diffusion is…

We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…

Dynamical Systems · Mathematics 2017-10-18 Shousuke Ohmori

By studying a modified (unbiased) quantum multibaker map, we were able to obtain a {\em finite} asymptotic quantum current without a classical analogue. This result suggests a general method for the design of {\em purely} quantum ratchets,…

Quantum Physics · Physics 2009-11-13 Leonardo Ermann , Gabriel G. Carlo , Marcos Saraceno

One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a…

Chaotic Dynamics · Physics 2023-01-25 Steven Tomsovic , Juan Diego Urbina , Klaus Richter

Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…

General Physics · Physics 2020-09-07 Jihad Asad , P. Mallick , B. Rath , M. E. Samei , Prachiparava Mohapatra , Hussein Shanak , Rabab Jarrar

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…

Astrophysics · Physics 2007-05-23 Henry E. Kandrup , Steven J. Novotny

In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…

Chaotic Dynamics · Physics 2022-07-19 Domenico Lippolis

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion…

Chaotic Dynamics · Physics 2007-05-23 Itzhack Dana , Vladislav E. Chernov

For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…

Dynamical Systems · Mathematics 2012-04-09 Amadeu Delshams , Marian Gidea , Pablo Roldan

The interplay between chaotic tunneling and dynamical localization in mixed phase space is investigated. Semiclassical analysis using complex classical orbits reveals that tunneling through torus regions and transport in chaotic regions are…

Chaotic Dynamics · Physics 2009-10-09 Akiyuki Ishikawa , Atushi Tanaka , Akira Shudo