Yi-Chiuan Chen, Wei-Ting Lin
Family of Smale-Williams Solenoid Attractors as Orbits of Differential Equations: Exact Solution and Conjugacy
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ABSTRACT. We show that the family of the Smale-Williams solenoid attractors parameterized by its contraction rate can be characterized as a solution of a differential equation. The exact formula describing the attractor can be obtained by solving the differential equation subject to an explicitly given initial condition. Using the formula, we present a simple and explicit proof that the dynamics on the solenoid is topologically conjugate to the shift on the inverse limit space of the expanding map t--> mt mod1 for some integer m at least 2 and to a suspension over the adding machine.