Dynamics of coupled symplectic map

• Grant number: 24/20417-8
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: March 27, 2025
• End date: March 26, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Iberê Luiz Caldas
• Grantee: Leonardo Costa de Souza
• Supervisor: Murilo da Silva Baptista
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Aberdeen, Scotland
• Associated to the scholarship: 23/16146-6 - Dynamics and transport in nonlinear symplectic map lattices, BP.PD

Abstract

This project proposes to investigate the dynamics and transport phenomena in Hamiltonian systems with many degrees of freedom. The study will focus on a lattice of coupled symplectic maps, where the coupling is non-local, and where the coupling strength follows a power-law dependence on the distance within the lattice. We will analyze diffusion as a function of network size and coupling strength. Additionally, our investigation will explore the formation of orbit cluster regions, which represent spatial coherent structures emerging from the dynamical system. The cluster regions are associated with the stickiness of chaotic trajectories near persistent periodic islands. To quantify this stickiness, we will employ a recurrence time entropy approach. Moreover, we will investigate the production and transfer of energy and information between the sites of the lattice, using the concept of mutual information rate.