Robust unbounded chaotic attractors in 1D discontinuous maps

Roya Makrooni, Neda Abbasi, Mehdi Pourbarat and Laura Gardini ()
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Roya Makrooni: Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
Neda Abbasi: Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
Mehdi Pourbarat: Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

No 1501, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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)
Pages: 14 pages
Date: 2015, Revised 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_15_01.pdf First version, 2015 (application/pdf)

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Journal Article: Robust unbounded chaotic attractors in 1D discontinuous maps (2015)
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