Chaotic Dynamics in the Vertically Driven Planar Pendulum

Lakshmi Burra ()
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Lakshmi Burra: Jawaharlal Nehru Technological University, Department of Mathematics

Chapter Chapter 3 in Chaotic Dynamics in Nonlinear Theory, 2014, pp 55-77 from Springer

Abstract: Abstract As a first application, we prove the presence of chaotic dynamics for a vertically driven planar pendulum. The theory of topological horseshoes and linked twist maps developed so far, along with phase-plane analysis, are used to show the presence of chaotic dynamics. We propose, in the general setting of topological spaces, a definition of two-dimensional oriented cell and consider maps which possess a property of stretching along the paths with respect to oriented cells. For these maps, we prove some theorems on the existence of fixed points, periodic points, and sequences of iterates, which are chaotic in a suitable manner. Our results, motivated by the study of the Poincaré map associated to some nonlinear equations, extend and improve some recent work.

Keywords: Poincaré map; Phase-plane analysis; Heteroclinic orbits; Oriented rectangles. (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-2092-3_3

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DOI: 10.1007/978-81-322-2092-3_3

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