Glendinning, Paul (2015) Bifurcation from stable fixed point to two-dimensional attractor in the border collision normal form. [MIMS Preprint]
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Abstract
The border collision normal form is a family of continuous two-dimensional piecewise smooth maps describing dynamics close to a critical parameter at which a fixed point intersects the switching surface. It is well known that if the fixed point is stable on one side of the bifurcation point then after the bifurcation the system may have stable periodic orbits and/or chaotic attractors with a quasi-one dimensional structure (robust chaos). We show that it is also possible to have a robust transition from a stable fixed point to an attractor with topological dimension two, i.e. the highest dimension possible in the phase space
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | {bifurcation, piecewise smooth dynamics, invariant measures, border collision, normal form |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory |
| Depositing User: | Professor Paul Glendinning |
| Date Deposited: | 17 Feb 2015 |
| Last Modified: | 20 Oct 2017 14:13 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2251 |
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