Comments on the Bifurcation Structure of 1D Maps

V.N. Belykh, Erik Mosekilde

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory, are called into attention.
Original languageEnglish
JournalOpen Systems and Information Dynamics
Volume4
Pages (from-to)379-392
ISSN1230-1612
Publication statusPublished - 1997

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