Weak universality in two-dimensional transitions to chaos
- 5 July 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 71 (1) , 58-61
- https://doi.org/10.1103/physrevlett.71.58
Abstract
Two rational numbers are associated to each periodic orbit of Smale’s horseshoe, and practical algorithms are given for their calculation. Using these quantities, it is possible to decide in many cases whether or not a given orbit must always be created after some other given orbit in any two-dimensional transition to chaos. A statement of ‘‘weak universality’’ for the bifurcation sequence as a whole is formulated.Keywords
This publication has 9 references indexed in Scilit:
- Remarks on the symbolic dynamics for the Hénon mapPhysics Letters A, 1992
- Topological and metric properties of Hénon-type strange attractorsPhysical Review A, 1988
- An analog of Sharkovski’s theorem for twist mapsContemporary Mathematics, 1988
- Generalizations of a theorem of Sarkovskii on orbits of continuous real-valued functionsDiscrete Mathematics, 1987
- Knotted periodic orbits in suspensions of Smale's horseshoe: Torus knots and bifurcation sequencesArchive for Rational Mechanics and Analysis, 1985
- Bifurcations of one- and two-dimensional mapsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1984
- Simple models for bifurcations creating horseshoesJournal of Statistical Physics, 1983
- Lyapunov exponents, entropy and periodic orbits for diffeomorphismsPublications mathématiques de l'IHÉS, 1980
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967