14-41 Yi-Chiuan Chen, Wei-Ting Lin

Family of Smale-Williams Solenoid Attractors as Orbits of Differential Equations: Exact Solution and Conjugacy (385K, PDF) May 17, 14

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

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.

Files: 14-41.src( 14-41.keywords , Formula_Solenoid_25April2014.pdf.mm )