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 language | English |
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Journal | Open Systems and Information Dynamics |
Volume | 4 |
Pages (from-to) | 379-392 |
ISSN | 1230-1612 |
DOIs | |
Publication status | Published - 1997 |