Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics. Twist correspond to Hamiltonians for which velocity is a monotonic function canonical momentum. have Lagrangian variational formulation. One-parameter families twist typically exhibit full range possible dynamics-from simple or integrable motion complex chaotic One class orbits, minimizing can be found throughout...

A particle in a chaotic region of phase space can spend long time near the boundary regular since transport there is slow. This "stickiness" regions thought to be responsible for previous observations numerical experiments long-time algebraic decay survivial probability, i.e., survival probability $\ensuremath{\sim}{t}^{\ensuremath{-}z}$ large $t$. paper presents global model such systems and demonstrates essential role infinite hierarchy small islands interspersed region. Results $z$ are discussed.

The theory of transport in nonlinear dynamics is developed terms "leaky" barriers which remain when invariant tori are destroyed. A critical exponent for times across destroyed obtained explains numerical results Chirikov. combined effects many lead to power-law decay correlations observed computations.

The two-component fluid equations describing electron-drift and ion-acoustic waves in a nonuniform magnetized plasma are shown to possess nonlinear two-dimensional solitary wave solutions. In the presence of magnetic shear, radiative shear damping is exponentially small Ls/Ln for drift waves, contrast linear waves.

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition between phase space. This paper surveys the considerable progress on this problem over past thirty years. Primary measures of for volume-preserving maps include exiting and incoming fluxes region. For area-preserving maps, impeded by curves formed invariant manifolds that form partial barriers, e.g., stable unstable bounding resonance zone cantori, remnants destroyed...

The ionization of hydrogen can be treated by classical theory when the initial quantum number is large and photon energy small. Classically, electron motion stochastic for high intensities resulting diffusion lead to ionization. However, Casati et al. [Phys. Rev. Lett. 57, 823 (1986)] have found that threshold often higher than stochasticity. We present here a heuristic explanation: stochasticity will suppressed phase-space area escaping through cantori each period electric field small...

This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular, between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold’s circle map, which there is a universal power law the fraction nonresonant as function amplitude nonlinearity. Our methods give more precise calculation coefficients this law. For we show no such any orbits. However, find different categories maps with qualitatively similar...

The authors derive a criterion for the non-existence of invariant Lagrangian graphs symplectic twist maps an arbitrary number degrees freedom, interpret it geometrically, and apply to four-dimensional example.

A ``class''-c orbit is one that rotates around a periodic of class c-1 with some definite frequency. This contrasts the ``level'' which number elements in continued-fraction expansion its Level renormalization conventionally used to study structure quasiperiodic orbits. The scaling orbits encircling other area-preserving maps discussed here. Renormalization fixed points p/q bifurcations are found and exponents determined. Fixed for q>2 correspond self-similar islands islands. Frequencies...

A theory of drift wave turbulence is presented based on a low-density gas solitons. The Gibb’s ensemble for the ideal used to calculate dynamical scattering form factor S(k,ω). In contrast renormalized theory, spectrum has broad frequency component with Δω proportional fluctuation level δne/n0 at fixed k and peaks ω≳kyvde.

The statistical properties of periodic impulse maps may be obtained from the characteristic functions. Series representations for functions, force correlations, and momentum diffusion coefficient are presented. These results applied to sawtooth map integer values perturbation parameter $\ensuremath{\epsilon}$, in which case series summed explicitly. It is found that has quasilinear value $|\ensuremath{\epsilon}+2|\ensuremath{\ge}2$, it vanishes $\ensuremath{\epsilon}=\ensuremath{-}2$ -1,...