Piecewise Linear Bidimensional Maps as Models of Return Maps for 3D Diffeomorphisms
The goal of this paper is to study the dynamics of a simple family of piecewise linear maps in dimension two, that we call Expanding Baker Maps (EBM), which is a simplified model of a quadratic limit return map which appears in the study of certain homoclinic bifurcations of two-parameter families of three-dimensional dissipative diffeomorphisms. In spite of its simplicity the EBM capture some of the more relevant dynamics of the quadratic family, specially that related to the evolution of 2D strange attractors.
KeywordsLyapunov Exponent Periodic Point Strange Attractor Critical Line Positive Lyapunov Exponent
This work has been supported by the MEC grants MTM2009-09723 and MTM2011-22956 and the CIRIT grant 2009 SGR 67.