Displaying similar documents to “Inverse Limits, Economics, and Backward Dynamics.”

Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets

Chris Good, Brian E. Raines (2006)

Fundamenta Mathematicae

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We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.

Attractors and Inverse Limits.

James Keesling (2008)

RACSAM

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This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.

Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities

Chris Good, Robin Knight, Brian Raines (2006)

Fundamenta Mathematicae

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We examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional nonhyperbolic sets (inverse limits of finite graphs), particularly when those inhomogeneities form a countable set. Using tools from descriptive set theory we prove a surprising restriction on the topological structure of these invariant sets if the map satisfies a weak...

Economic system dynamics.

McCauley, Joseph L., Küffner, Cornelia M. (2004)

Discrete Dynamics in Nature and Society

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Devil's staircase route to chaos in a forced relaxation oscillator

Lluis Alsedà, Antonio Falcó (1994)

Annales de l'institut Fourier

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We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance...