Chaotic Transport in Time-Dependent Symplectic Maps

Chaotic particle transport in time-dependent Rayleigh-Bénard convection.

Chaotic time-dependent billiards

A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are investigated. In the phase plane areas corresponding to decrease and increase of the velocity of billiard particles are found. Average velocities of the particl...

Symplectic maps

Here Dfij = ∂fi/∂zj is the Jacobian matrix of f , J is the Poisson matrix, and I is the n × n identity matrix. Equivalently, Stokes’ theorem can be used to show that the loop action, A[γ] = ∮ γ pdq, is preserved by f for any contractible loop γ on X. If f preserves the loop action for all loops, even those that are not contractible, then it is exact symplectic. When n = 1, the symplectic condit...

Watermarking Scheme Based on Multiple Chaotic Maps

a watermarking scheme for Grayscale image isproposed based on a family of the chaotic maps and discretecosine transform. Jacobian Elliptic mapis employed to encrypt ofwatermarked logo. Piecewise nonlinear chaotic map is also usedto determine the location of DCT coefficients for the watermarkembedding. The purpose of this algorithm is to improve theshortcoming of watermarking such as small key s...

Multidimensional Symplectic Separatrix Maps

We present formulas, describing the dynamics of an a priori unstable (initially hyperbolic) near-integrable Hamiltonian system in a neighborhood of stable and unstable asymptotic manifolds of a family of hyperbolic tori 1 Introduction