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Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…

Astrophysics · Physics 2009-10-30 Henry E. Kandrup

Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a…

Accelerator Physics · Physics 2009-11-10 Courtlandt L. Bohn , Ioannis V. Sideris

It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…

Dynamical Systems · Mathematics 2019-05-16 Mikhail B. Sevryuk

We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided into a grid of cells…

Chaotic Dynamics · Physics 2021-04-14 Črt Lozej , Marko Robnik

We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known…

Chaotic Dynamics · Physics 2017-01-09 M. Katsanikas , P. A. Patsis , G. Contopoulos

In the present article, we present a galactic gravitational model of three degrees of freedom, in order to investigate and reveal the behavior of orbits in a binary quasar system. The two quasars are hosted in a pair of interacting disk…

Astrophysics of Galaxies · Physics 2014-02-18 Euaggelos E. Zotos

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

A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.

Chaotic Dynamics · Physics 2009-11-07 K. Weibert , J. Main , G. Wunner

This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…

Astrophysics · Physics 2007-05-23 Henry E. Kandrup

The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and…

Chaotic Dynamics · Physics 2013-01-30 Marcelo S. Custódio , Cesar Manchein , Marcus W. Beims

We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or…

Astrophysics of Galaxies · Physics 2017-12-13 L. Chaves-Velasquez , P. A. Patsis , I. Puerari , Ch. Skokos , T. Manos

The statistics of Poincar\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this…

Chaotic Dynamics · Physics 2016-12-13 Steffen Lange , Arnd Bäcker , Roland Ketzmerick

We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…

Dynamical Systems · Mathematics 2015-06-19 Heather Reeve-Black , Franco Vivaldi

Dissipationless N-body models of rotating galaxies, iso-energetic to a non-rotating model, are examined as regards the mass in regular and in chaotic motion. The values of their spin parameters $\lambda$ are near the value $\lambda=0.22$ of…

Astrophysics · Physics 2009-09-29 N. Voglis , I. Stavropoulos , C. Kalapotharakos

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold.…

Dynamical Systems · Mathematics 2009-11-11 Denis Blackmore , Lu Ting , Omar Knio

In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a…

General Relativity and Quantum Cosmology · Physics 2024-01-01 Saikat Das , Suparna Roychowdhury

For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the…

Dynamical Systems · Mathematics 2020-05-12 Mikhail B. Sevryuk

We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…

Chaotic Dynamics · Physics 2017-09-28 Euaggelos E. Zotos

We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to…

Pattern Formation and Solitons · Physics 2009-11-13 Roy H. Goodman

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…

Dynamical Systems · Mathematics 2009-11-13 P. Glendinning , T. Jaeger , J. Stark