In this project, we present a proposal to study transport processes in different Hamiltonian systems. 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 form a Cantor set for area-preserving maps, and (ii) partial barriers that limit the resonance zones formed by the breaking of separatrices of an unstable periodic orbit. The initial proposal includes the study of three 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 non-twist standard map, which violates the twist condition locally, preventing the application of the KAM theorem and leading to the emergence of new phenomena. We will also analyze how particle transport depends on the geometry of a composition of two distinct billiards where the phase space is non-hierarchical. Finally, we intend to study the coherence and synchronization states of a network of coupled symplectic maps and the relationship between synchronization and transport in high-dimensional phase space.
News published in Agência FAPESP Newsletter about the scholarship: