Similarity Structure and Scaling Property of the Period-Adding Phenomena
Open Access
- 1 February 1983
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 69 (2) , 403-414
- https://doi.org/10.1143/ptp.69.403
Abstract
Period-adding sequence at the locking from torus to chaos is studied with the use of a one-dimensional mapping. Similarity and various scaling properties of each cycle are found numerically, which can be explained through a “phenomenological theory” based on the existence of the fixed point function. We classify the sequence into three cases. We also apply our theory to the case in which the sequence is a window among chaotic states.Keywords
This publication has 4 references indexed in Scilit:
- Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted studyCommunications in Mathematical Physics, 1982
- Critical behavior of a KAM surface: I. Empirical resultsJournal of Statistical Physics, 1982
- Intermittency in area-preserving mappingsPhysical Review A, 1982
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978