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Complex Dynamics and Thermodynamic Formalism

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


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. Dinâmica complexa e formalismo termodinâmico. 2011. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação São Carlos.

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