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010   $a81-322-2092-7
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100   $a20140910d2014      u|             0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aChaotic Dynamics in Nonlinear Theory$b[electronic resource] /$fby Lakshmi Burra
205   $a1st ed. 2014.
210  1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2014.
215   $a1 online resource (118 p.) 
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a81-322-2091-9 
320   $aIncludes bibliographical references and index.
327   $aChapter 1. Topological Considerations -- Chapter 2. Topological horseshoes and coin-tossing dynamics -- Chapter 3. Chaotic Dynamics in the vertically driven planar pendulum -- Chapter 4. Chaos in a pendulum with variable length.
330   $aUsing 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.
606   $aDynamics
606   $aErgodic theory
606   $aPartial differential equations
606   $aStatistical physics
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aPartial differential equations.
615  0$aStatistical physics.
615 14$aDynamical Systems and Ergodic Theory.
615 24$aPartial Differential Equations.
615 24$aApplications of Nonlinear Dynamics and Chaos Theory.
676   $a531.11
700   $aBurra$b Lakshmi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721178
906   $aBOOK
912   $a9910299987903321
996   $aChaotic dynamics in nonlinear theory$91410000
997   $aUNINA