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Author(s):
H.B. Stewart
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Title:
Application of Fixed Point Theory to Chaotic Attractors of Forced Oscillators
Date of publication:
Nov. 1990
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Key words:
Nonlinear dynamics, Chaotic attractor, Fixed point index, Euler characteristic.
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Abstract:
A review of the structure of chaotic attractors of periodically forced second-order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand.
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