Physics of Chaos in Hamiltonian Systems

  title={Physics of Chaos in Hamiltonian Systems},
  author={George Zaslavsky},

Hybrid quantum–classical chaotic NEMS


We review an approach to separatrix chaos that has allowed us to solve some significant problems by: (i) finding analytically the maximum width of the chaotic layer, a problem that lay unsolved for

Universal description of the resonant facilitation of the inter-separatrix chaos onset

  • S. SoskinR. Mannella
  • Physics
    2013 22nd International Conference on Noise and Fluctuations (ICNF)
  • 2013
We have developed a universal asymptotic description of the strong resonance-mediated facilitation of the onset of the inter-separatrix chaotic transport (IST) - a remarkable phenomenon discovered a

Estimating the size of the regular region of a topographically trapped vortex

We formulate a dynamically consistent two-layer quasigeostrophic model of geophysical flow using the concept of background currents which are characterized by a constant potential vorticity

Baroclinic multipole evolution in shear and strain

In a two-layer quasi-geostrophic model, the evolution of a symmetric baroclinic multipole, composed of a central vortex with strength μκ in the upper layer, and A satellites with strength κ in the

Dynamic switching of magnetization in driven magnetic molecules

We study the magnetization dynamics of a molecular magnet driven by static and variable magnetic fields within a semiclassical treatment. The underling analyzes is valid in a regime, when the energy

Stationary Hamiltonian transport with dc bias

The dynamics of a particle in a symmetric periodic potential under the influence of a time-periodic field is characterized by a mixed phase space with regular and chaotic components. An additional

Divergence of the chaotic layer width and strong acceleration of the spatial chaotic transport in periodic systems driven by an adiabatic ac force.

We show for the first time that a weak perturbation in a Hamiltonian system may lead to an arbitrarily wide chaotic layer and fast chaotic transport. This generic effect occurs in any spatially

Lévy scaling: the diffusion entropy analysis applied to DNA sequences.

It is proved that the DEA is the only method that always yields the correct scaling value, if the scaling condition applies and that the joint use of DEA and variance method allows to assess whether a time series is characterized by Lévy or Gauss statistics.

Dynamical mechanisms of dc current generation in driven Hamiltonian systems.

  • S. DenisovS. Flach
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
It is shown that the dc current is induced by the presence and desymmetrization of ballistic channels inside the stochastic layer of a system describing the motion of a particle in a one-dimensional potential in the presence of an ac time-periodic drive.



Chaos and Structures in Nonlinear Plasmas

This book develops the subject of nonlinear plasma physics from a general physics perspective. It begins with a description of nonlinear oscillations, the parametric instability, the pendulum, and

Symmetries, topology and resonances in Hamiltonian mechanics

I Hamiltonian Mechanics.- 1 The Hamilton Equations.- 2 Euler-Poincare Equations on Lie Algebras.- 3 The Motion of a Rigid Body.- 4 Pendulum Oscillations.- 5 Some Problems of Celestial Mechanics.- 6

Weak chaos and quasi-regular patterns

Part I. General Concepts: Hamiltonian dynamics Stability and chaos Part II. Dymanic Order and Choas: The stochastic layer Stochastic layer - stochastic sea transition The stochastic web Uniform web

An Introduction to the Fractional Calculus and Fractional Differential Equations

Historical Survey The Modern Approach The Riemann-Liouville Fractional Integral The Riemann-Liouville Fractional Calculus Fractional Differential Equations Further Results Associated with Fractional

Introduction to Probability

The articles [8], [9], [4], [7], [6], [2], [5], [1], and [3] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: E denotes a non empty set, a

Continued Fractions, Chicago, IL

  • 1964

Fractional Integrals and Derivatives and Their Applications, Translated by Harwood Academic Publishers. Minsk: Naukai Tekhnika

  • 1987

Quasi-crystals and Geometry

  • 1995