Bifurcation structure in the skew tent map and its application as a border collision normal form. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Sushko, I.; Avrutin, V.; Gardini, L.
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 4(2016)
• Page Start: 582
• Page End: 629
• Publication Date: 2016-04-02
• Subjects: Skew tent map -- border collision bifurcations -- border collision normal form -- homoclinic bifurcations -- bifurcations of chaotic attractors; 37E05 -- 37G35 -- 37N30; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2015.1113273
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : The goal of the present paper is to collect the results related to dynamics of a one-dimensional piecewise linear map widely known as the skew tent map. These results may be useful for the researchers working on theoretical and applied problems in the field of nonsmooth dynamical systems. In particular, we propose the complete description of the bifurcation structure of the parameter space of the skew tent map, providing the related proofs. It is also shown how these results can be used to classify border collision bifurcations in one-dimensional piecewise smooth maps.