Smooth linearization of hyperbolic fixed points

• Grant number: 08/02321-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2008
• End date: March 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daniel Smania Brandão
• Grantee: Jose Humberto Bravo Vidarte
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Given a hyperbolic fixed point of a diffeomorphism acting on a manifold, it is well know that by the Hartman-Grobman Theorem the dynamics close to this fixed point is topologically conjugate with its linear part. In general such conjugacy is not smooth. We will study conditions that implies the existence of smooth conjugacies (C^k, with a positive integer k) with either its linearization or a higher order normal form of the diffeomorphism at the fixed point. We will also study the dependence of this conjugacy with respect to a family of dynamical systems.

Academic Publications

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

VIDARTE, Jose Humberto Bravo. Smooth linearization of hiperbolic fixed points.. 2010. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.