Hidden dynamics for piecewise smooth maps

Paul Glendinning; Mike R Jeffrey

doi:10.1088/1361-6544/abe734

Hidden dynamics for piecewise smooth maps

Paul Glendinning, Mike R Jeffrey

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a hidden dynamics formulation of regularisation for piecewise smooth maps. This involves blowing up the discontinuity into an interval, but in contrast to piecewise smooth flows every preimage of the discontinuity needs to be blown up as well. This results in a construction similar to classic approaches to the Denjoy counterexample.

Original language	English
Article number	3184
Journal	Nonlinearity
Volume	34
Issue number	5
DOIs	https://doi.org/10.1088/1361-6544/abe734
Publication status	Published - 1 May 2021

Keywords

regularization
Sharkovskii's Theorem
piecewise smooth dynamics
hidden dynamics

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10.1088/1361-6544/abe734

https://iopscience.iop.org/article/10.1088/1361-6544/abe734/pdf

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title = "Hidden dynamics for piecewise smooth maps",

abstract = "We develop a hidden dynamics formulation of regularisation for piecewise smooth maps. This involves blowing up the discontinuity into an interval, but in contrast to piecewise smooth flows every preimage of the discontinuity needs to be blown up as well. This results in a construction similar to classic approaches to the Denjoy counterexample.",

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AB - We develop a hidden dynamics formulation of regularisation for piecewise smooth maps. This involves blowing up the discontinuity into an interval, but in contrast to piecewise smooth flows every preimage of the discontinuity needs to be blown up as well. This results in a construction similar to classic approaches to the Denjoy counterexample.

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JO - Nonlinearity

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Hidden dynamics for piecewise smooth maps

Abstract

Keywords

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