Family of Smale-Williams Solenoid Attractors as Solutions of Differential Equations: Exact Formula and Conjugacy.

We show that the family of the Smale-Williams solenoid attractors parameterized by its contraction rate can be characterized as solutions of a set of differential equations. The exact formula describing the attractor can be obtained by solving the differential equations subject to explicitly given initial conditions. Using the formula, we present in this note a simple and explicit proof of the result that the dynamics on the solenoid is topologically conjugate to the shift on the inverse limit space of the expanding map t ↦ mt mod 1 for some integer m ≥ 2 and to a suspension over the adding machine. [ABSTRACT FROM AUTHOR]