A. Marqu s-Lobeiras, A. Pumari o, J.A. Rodr guez, E. Vigil
Splitting and coexistence of 2-D strange attractors in a general family of Expanding Baker Maps
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ABSTRACT. We consider a two-parameter family $\Gamma_{a, heta}$ of Expanding Baker Maps on the plane, being $a > 1$ and $0< heta<\pi$ an expansion rate and a rotation angle, respectively. We prove that $\Gamma_{a, heta}$ exhibits strange attractors for every $a$ sufficiently close to $1$. We also study how such attractors may split into other ones of a larger number of connected pieces as $a$ decreases to $1$ and $ heta/\pi$ is a rational number. The study of the family $\Gamma_{a, heta }$ is strongly motivated by the rich dynamics observed for the quadratic family $T_{a,b}(x,y)=(a+y^{2},x+by)$.