By Lakshmi Burra

Using phase–plane research, findings from the speculation of topological horseshoes and linked-twist maps, this e-book provides a singular technique to end up the life of chaotic dynamics. In dynamical structures, complicated habit in a map will be indicated by way of showing the life of a Smale-horseshoe-like constitution, both for the map itself or its iterates. This frequently calls for a few assumptions concerning the map, similar to a diffeomorphism and a few hyperbolicity stipulations. during this textual content, much less stringent definitions of a horseshoe were advised in order to reproduce some geometrical beneficial properties standard of the Smale horseshoe, whereas leaving out the hyperbolicity stipulations linked to it. This results in the examine of the so-called topological horseshoes. The presence of chaos-like dynamics in a vertically pushed planar pendulum, a pendulum of variable size, and in different extra normal similar equations can also be proved.

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