Arnold Diffusion in A Priori Chaotic Symplectic Maps

Arnold diffusion in Hamiltonian Systems 1: a priori Unstable Case

By using variational method and under generic conditions we show that Arnold diffusion exists in a priori unstable and time-periodic Hamiltonian systems with multiple degrees of freedom.

Modulated Diffusion for Symplectic Maps

Chaotic diffusion on periodic orbits: the perturbed Arnold cat map.

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold 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 coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-numbe...

Chaotic Diffusion in Multidimensional Conservative Maps

In the present paper, we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in the phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a multidimensional conservative map that would be r...

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

In the present paper we consider the case of a general Cr+2 perturbation, for r large enough, of an a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom, and we provide explicit conditions on it, which turn out to be C2 generic and are verifiable in concrete examples, which guarantee the existence of Arnold diffusion. This is a generalization of the result in Delshams et al., Mem....