Mechanism of transport in Hamiltonian systems

Abstract

The mechanisms of transport phenomena in Hamiltonian systems with mixed phase space are described through (i) remnants of Kolmogorov-Arnold-Moser (KAM) tori, called cantori, which are a Cantor set, and (ii) partial barriers that limit the resonance zones formed by the breaking of separatrices of an unstable periodic orbit. We propose the study of two low-dimensional Hamiltonian systems and one high-dimensional system, aiming to provide a comprehensive overview of transport processes in Hamiltonian systems with different characteristics. We will consider an extension of the nontwist standard map, which violates the twist condition locally, preventing the application of the KAM theorem and leading to the emergence of new phenomena. We also consider the extension of a family of Hamiltonian mappings by including a second perturbation. Finally, we intend to study the transport processes of a 4D symplectic mapping which exhibits completely new dynamics given the high dimensionality of phase space.