|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.