Piecewise linear discontinuous double coverings of the circle
HTML articles powered by AMS MathViewer
- by Roza Galeeva and Charles Tresser PDF
- Proc. Amer. Math. Soc. 118 (1993), 285-291 Request permission
Abstract:
In his study of a particular Lorenz-like semiflow, S. F. Kennedy introduced a two-parameter family of endomorphisms of the circle with two marked points. These are piecewise affine double coverings of the circle with a pair of discontinuities, which all have topological entropy $\log 2$. We answer the question Kennedy raised about when two such maps are topologically conjugate.References
- Michael Benedicks and Lennart Carleson, On iterations of $1-ax^2$ on $(-1,1)$, Ann. of Math. (2) 122 (1985), no. 1, 1–25. MR 799250, DOI 10.2307/1971367 R. Galeeva, Kneading sequences of piecewise bimodal maps, Chaos (to appear). S. F. Kennedy, A Lorenz-like strange attractor, Ph.D. thesis, Northwestern University, 1988. —, The topology of the periodic points set of a family of circle maps, preprint, Univ. of Delaware, 1989.
- John Milnor and William Thurston, On iterated maps of the interval, Dynamical systems (College Park, MD, 1986–87) Lecture Notes in Math., vol. 1342, Springer, Berlin, 1988, pp. 465–563. MR 970571, DOI 10.1007/BFb0082847
- M. Misiurewicz and E. Visinescu, Kneading sequences of skew tent maps, Ann. Inst. H. Poincaré Probab. Statist. 27 (1991), no. 1, 125–140 (English, with French summary). MR 1098567
- John Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 59–72. MR 556582
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 285-291
- MSC: Primary 58F08; Secondary 58F03
- DOI: https://doi.org/10.1090/S0002-9939-1993-1150650-9
- MathSciNet review: 1150650