Dissipative particles under the action of expanding dynamical systems

• Grant number: 22/05300-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2022
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daniel Smania Brandão
• Grantee: Pedro Augusto da Silva Morelli
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems, AP.TEM
• Associated scholarship(s): 24/10617-0 - Anisotropic Spaces and Dynamical Systems, BE.EP.DR

Abstract

We will study the evolution under the action of a dynamic expanding or expanding system by pieces of sets (finite or infinite) of charged particles (which can be positive or negative) when such charges have a half-life, that is, their charges dissipate exponentially over time. The half-life may be either constant over the phase space or depend on the position of the particle. You will need to regularly release newly charged particles into phase space for the study to become interesting. In particular, we will study the existence of stable configurations and their statistical properties using tools such as ergodic theory and thermodynamic formalism (transfer operators)