Periodic points of disk homeomorphisms having a pseudo-Anosov component

Hokkaido Mathematical Journal

Volumn 27, Issue 2, 1998, Pages 423-455

  Matsuoka, Takashi ^a  

^a NARUTO UNIVERSITY OF EDUCATION   (Japan)

Author keywords

Braid; Disk homeomorphism; Periodic point; Pseudo Anosov homeomorphism

Indexed keywords

EID: 0037481362     PISSN: 03854035     EISSN: None     Source Type: Journal    
DOI: 10.14492/hokmj/1351001293     Document Type: Article

References (22)

1. Bowen R., Entropy and the fundamental group. The Structure of Attractors in Dynamical Systems, Lecture Notes in Math. 668, Springer-Verlag, Berlin, Heidelberg, New York, 1978, 21-29.
2. Brown R., The Lefschetz Fixed Point Theorem. Scott-Foresman, Chicago, 1971.
3. Boyland P., Braid types and a topological method of proving positive entropy. preprint.
4. Boyland P., Topological methods in surface dynamics. Topology and its Appl. 58 (1994), 223-298.
5. Boyland P., Isotopy stability of dynamics on surfaces, preprint.
6. Fathi A., Laudenbach F. and Poénaru V., Travaux de Thurston sur les surfaces. Astérisque 66-67 (1979).
7. Franks J., Recurrence and fixed points of surface homeomorphisms. Ergod. Th. and Dynarn. Sys. 8* (1988), 99-107.
8. Franks J. and Misiurewicz M., Cycles for disk homeomorphisms and thick trees. Nielsen Theory and Dynamical Systems, Contemp. Math. 152. Amer. Math. Soc., Providence, 1993, 69-139.
9. Gambaudo J.M. and Llibre J., A note on the periods of surface homeomorphisms. J. Math. Anal. Appl. 177 (1993), 627-632.
10. Gambaudo J.M., van Strien S. and Tresser C., Vers un ordre de Sarkovskii pour les plongements du disque préservant l’orientation. C.R. Acad. Sci. Paris Sér. 1 310 (1990), 291-294.
11. Guaschi J., Pseudo-Anosov braid types of the disc or sphere of low cardinality imply all periods. J. London Math. Soc. 50 (1994), 594-608.
12. Guaschi J., Lefschetz numbers of periodic orbits of pseudo-Anosov homeomorphisms. Math. Proc. Camb. Phil. Soc. 115 (1994), 121-132.
13. Hardy G.H. and Wright E.M., An Introduction to the Theory of Numbers. Fifth Edition. Oxford Univ. Press, Oxford, 1979.
14. Jiang B., Lectures on Nielsen Fixed Point Theory. Contemp. Math. 14, Amer. Math. Soc., Providence, 1983.
15. Jiang B., Nielsen theory for periodic orbits and applications to dynamical systems. Nielsen Theory and Dynamical Systems, Contemp. Math. 152. Amer. Math. Soc., Providence, 1993, 183-202.
16. Jiang B., Estimation of the number of periodic orbits. Pacific J. Math. 172. (1996), 151-185.
17. Jiang B. and Guo J., Fixed points of surface diffeomorphisms. Pacific J. Math. 160 (1993), 67-89.
18. Kolev B., Periodic orbits of period 3 in the disc. Nonlinearity 7 (1994), 1067-1071.
19. Llibre J. and MacKay R.S., Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods. Math. Proc. Camb. Phil. Soc. 112 (1992), 539-549.
20. Matsuoka, T., Braids of periodic points and a 2-dimensional analogue of Sharkovskii’s ordering. Dynamical Systems and Nonlinear Oscillations (ed. G. Ikegami), World Sci. Adv. Ser. in Dynam. Sys. 1, World Sci., Singapore, 1986, 58-72.
21. Matsuoka T., Braid type of the fixed point set for orientation-preserving embeddings on the disk. Tokyo J. Math. 18 (1995), 457-472.
22. Thurston W.P., On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. 19 (1988), 417-431.