Nonsmooth one-dimensional maps: some basic concepts and definitions. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Sushko, I.; Gardini, L.; Avrutin, V.
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 12(2016)
• Page Start: 1816
• Page End: 1870
• Publication Date: 2016-12-01
• Subjects: Piecewise smooth map -- border collision bifurcation -- homoclinic bifurcation -- bifurcation structure; 37E05 -- 37G35 -- 37N30; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2016.1248426
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : The main purpose of the present survey is to contribute to the theory of dynamical systems defined by one-dimensional piecewise monotone maps . We recall some definitions known from the theory of smooth maps, which are applicable to piecewise smooth ones, and discuss the notions specific for the considered class of maps. To keep the presentation clear for the researchers working in other fields, especially in applications, many examples are provided. We focus mainly on the notions and concepts which are used for the investigation of various kinds of attractors of a map and related bifurcation structures observed in its parameter space.