Robust unbounded chaotic attractors in 1D discontinuous maps

Roya Makrooni, Neda Abbasi, Mehdi Pourbarat and Laura Gardini ()

Chaos, Solitons & Fractals, 2015, vol. 77, issue C, 310-318

Abstract: In this paper we prove the existence of full measure unbounded chaotic attractors which are persistent under parameter perturbation (also called robust). We show that this occurs in a discontinuous piecewise smooth one-dimensional map f, belonging to the family known as Nordmark’s map. To prove the result we extend the properties of a full shift on a finite or infinite number of symbols to a map, here called Baker-like map with infinitely many branches, defined as a map of the interval I=[0,1] into itself with infinitely branches due to expanding functions with range I except at most the rightmost one. The proposed example is studied by using the first return map in I, which we prove to be chaotic in I making use of the border collision bifurcations curves of basic cycles. This leads to a robust unbounded chaotic attractor, the interval (−∞,1], for the map f.

Keywords: Unbounded chaotic attractors; Robust full measure chaotic attractors; Piecewise smooth systems; Full shift maps; Border collision bifurcations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:77:y:2015:i:c:p:310-318

DOI: 10.1016/j.chaos.2015.06.012

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