Frequency locking on the boundary of the barycentre set

Experimental Mathematics

Volumn 9, Issue 2, 2000, Pages 309-317

  Jenkinson, Oliver ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034348604     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2000.10504655     Document Type: Article

References (17)

1. J. Berstel, “Recent results in Sturmian words”, pp. 13-24 in Developments in language theory, II (Magdeburg, 1995), edited by J. Dassow et al., World Sci. Publishing, River Edge, NJ, 1996.
2. T. Bousch, “Le poisson n’a pas d’aretes”, preprint, Laboratoire de Topologie et Dynamique, Universite d’Orsay, 1998. To appear in Ann. IHP Proba. Stat.
3. P. L. Boyland, “Bifurcations of circle maps: Arnol’d tongues, bistability and rotation intervals”, Comm. Math. Phys. 106: 3 (1986), 353-381.
4. T. C. Brown, “Descriptions of the characteristic sequence of an irrational”, Canad. Math. Bull. 36: 1 (1993), 15-21.
5. S. Bullett and P. Sentenac, “Ordered orbits of the shift, square roots, and the devil’s staircase”, Math. Proc. Cambridge Philos. Soc. 115: 3 (1994), 451-481.
6. J.-M. Gambaudo, O. Lanford, III, and C. Tresser, “Dynamique symbolique des rotations”, C. R. Acad. Sci. Paris Ser. I Math. 299: 16 (1984), 823-826.
7. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fifth ed., Oxford University Press, New York, 1979.
8. B. R. Hunt and E. Ott, “Optimal periodic orbits of chaotic systems occur at low period”, Phys. Rev. E 54 (1996), 328-337.
9. O. Jenkinson, Conjugacy rigidity, cohomological triviality, and barycentres of invariant measures, Ph.D. thesis, Warwick University, 1996. See http://www.maths.qmw.ac.uk/-omj/.
10. A. Katok and B. Hassel- blatt, Introduction to the modem theory of dynamical systems, Cambridge University Press, Cambridge, 1995.
11. M. Morse and G. A. Hed- lund, “Symbolic dynamics, II: Sturmian trajectories”, Amer. J. Math. 62 (1940), 1-42.
12. S. Newhouse, J. Palis, and F. Takens, “Bifurcations and stability of families of diffeomorphisms”, Publ. Math. Inst. Hautes Etudes Sci. 57 (1983), 5-71.
13. H. L. Royden, Real analysis, 3rd ed., Macmillan, New York, 1988.
14. C. Series, “The geometry of Markoff numbers”, Math. Intelligencer 7: 3 (1985), 20-29.
15. P. Veerman, “Symbolic dynamics and rotation numbers”, Phys. A 134: 3 (1986), 543-576.
16. P. Veerman, “Symbolic dynamics of order-preserving orbits”, Phys. D 29: 1-2 (1987), 191-201.
17. P. Walters, An introduction to ergodic theory, Springer, New York, 1982.