This leads to the study of the so-called topological horseshoes.
Books > Mathematics.
This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions.
In Nonlinear Chaotic Theory Dynamics.
InÂ dynamical systems, complex behavior in aÂ map can be indicated by showingÂ the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates.
The presence of chaos-like dynamics in a vertically driven planar pendulum, a pendulum of variable length, and in other more general related equations is also proved.
In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce someÂ geometrical features typical of the Smale horseshoe, while leaving out the hyperbolicity conditions associated with it.
Using phaseâplane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics
Books > Mathematics
Chaotic Dynamics In Nonlinear Theory
Specifications of Chaotic Dynamics In Nonlinear Theory
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