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Tinkerbell Is Chaotic.
- Source :
-
SIAM Journal on Applied Dynamical Systems . 2011, Vol. 10 Issue 4, p1480-1501. 22p. - Publication Year :
- 2011
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15360040
- Volume :
- 10
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Applied Dynamical Systems
- Publication Type :
- Academic Journal
- Accession number :
- 75015401
- Full Text :
- https://doi.org/10.1137/100819011