Tinkerbell is chaotic

Alexandre Goldsztejn, Wayne Hayes, Pieter Collins

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Shadowing is a method of backward error analysis that plays a important role in hyperbolic dynamics. In this paper, the shadowing by containment framework is revisited, including a new shadowing theorem. This new theorem has several advantages with respect to existing shadowing theorems: It does not require injectivity or differentiability, and its hypothesis can be easily verified using interval arithmetic. As an application of this new theorem, shadowing by containment is shown to be applicable to infinite length orbits and is used to provide a computer assisted proof of the presence of chaos in the well-known noninjective Tinkerbell map.
Original languageEnglish
Pages (from-to)1480-1501
Number of pages22
JournalSiam Journal on Applied Dynamical Systems
Volume10
Issue number4
DOIs
Publication statusPublished - 2011

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