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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Chaotic Dynamics in Nonlinear Theory (Paperback, Softcover reprint of the original 1st ed. 2014)
Loot Price: R1,495
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Chaotic Dynamics in Nonlinear Theory (Paperback, Softcover reprint of the original 1st ed. 2014)
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Using phase-plane 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. In dynamical systems,
complex behavior in a map can be indicated by showing the existence
of a Smale-horseshoe-like structure, either for the map itself or
its iterates. This usually requires some assumptions about the map,
such as a diffeomorphism and some hyperbolicity conditions. In this
text, less stringent definitions of a horseshoe have been suggested
so as to reproduce some geometrical features typical of the Smale
horseshoe, while leaving out the hyperbolicity conditions
associated with it. This leads to the study of the so-called
topological horseshoes. 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.
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