Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on
Smale’s famous example, provide a rigorous way to study chaos in dynamical
systems. This program is written according to the algorithm proposed in the
paper, which has submitted to DDSN “An algorithm to automatically detect Smale
horseshoes”. The program includes the codes for the four examples in that paper
(the Duffing map, the Hénon map, the Ikeda map, and the Lozi map).
How does the program work?
The file “FindPeirod.m” is used to get the period obits and find the saddle
points, as well as the eigenvalues and eigenvectors of the Jacobian at those
points. You may pick one, copy it into “HorseshoeFindAuto_demo.m” .
The file “HorseshoeFindAuto_demo.m” demonstrates the step of the algorithm in
that paper. For an animation set the variable “Anm” to be 1 second.
Key words: Chaos, Smale horseshoe, chaotic maps, topological horseshoe