On the scaling properties of the period-increment scenario in dynamical systems
type: Item
instance of: scholarly article
title: On the scaling properties of the period-increment scenario in dynamical systems
zbMATH Open document ID: 0961.37014
DOI: 10.1016/S0960-0779(99)00071-5
published in: Chaos, Solitons and Fractals
publication date: 2001-05-17T00:00:00Z
review text: Period doubling scenarios, or more general period-multiplying scenarios are widely known, and universal scaling constants have been found, e.g., for unimodal maps. An arithmetic sequence of periods occurs in period increment scenarios, where in each bifurcation the number of periodic orbits changes by an additive constant. In this paper, the authors give two very simple examples of discontinuous maps of an interval that exhibit the latter behaviour, and for which bifurcation points and scaling constants can be computed analytically. However, these constants are not universal in the second example; they depend on the parameters.
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37E20
zbMATH DE Number: 1501100
zbMATH Keywords: period-increment bifurcation cascade
zbMATH Keywords: scaling constants
author: Viktor Avrutin
author: Michael Schanz
reviewed by: Jens D. M. Rademacher
MaRDI profile type: Publication
Wikidata QID: Q57627476
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description: scientific article; zbMATH DE number 1501100