Wave numbers for unimodal maps
- 1 March 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 37 (5) , 1827-1830
- https://doi.org/10.1103/physreva.37.1827
Abstract
The wave number for one-dimensional maps is introduced. For unimodal maps this new concept is a counterpart to the winding number for circle maps. Its dependence on the tuning parameter, in particular, some scaling behavior, is discussed.Keywords
This publication has 8 references indexed in Scilit:
- Transition to chaos by interaction of resonances in dissipative systems. I. Circle mapsPhysical Review A, 1984
- Complete Devil's Staircase, Fractal Dimension, and Universality of Mode- Locking Structure in the Circle MapPhysical Review Letters, 1983
- Fine Structure of Phase LockingPhysical Review Letters, 1982
- Intermittent transition to turbulence in dissipative dynamical systemsCommunications in Mathematical Physics, 1980
- The universal metric properties of nonlinear transformationsJournal of Statistical Physics, 1979
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978
- Simple mathematical models with very complicated dynamicsNature, 1976
- On finite limit sets for transformations on the unit intervalJournal of Combinatorial Theory, Series A, 1973