Complex Dynamics and Thermodynamic Formalism

• Grant number: 08/07356-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2009
• End date: February 28, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daniel Smania Brandão
• Grantee: Carlos Alberto Siqueira Lima
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Given a complex dynamical system, as for instance a conformal iterated dynamical system, we can associate to it various dynamically defined mathematical objets, as its maximal invariant set and its invariant measures. It is natural to ask about the behaviour of such objects when we perturb the dynamical system. We are specially interested in the differentiability of the Hausdorff dimension of maximal invariant sets and invariant measures with respect to the parameter in a smooth family of dynamical systems. The main tool in this study will be the so called thermodynamical formalism.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LIMA, Carlos Alberto Siqueira. Complex dynamics and thermodynamic formalism. 2011. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.