The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero

J. M. Gambaudo; S. Van Strien; C. Tresser

Annales de l'I.H.P. Physique théorique (1989)

  • Volume: 50, Issue: 3, page 335-356
  • ISSN: 0246-0211

How to cite

top

Gambaudo, J. M., Van Strien, S., and Tresser, C.. "The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero." Annales de l'I.H.P. Physique théorique 50.3 (1989): 335-356. <http://eudml.org/doc/76451>.

@article{Gambaudo1989,
author = {Gambaudo, J. M., Van Strien, S., Tresser, C.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {periodic orbits; orientation preserving embeddings; zero topology entropy},
language = {eng},
number = {3},
pages = {335-356},
publisher = {Gauthier-Villars},
title = {The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero},
url = {http://eudml.org/doc/76451},
volume = {50},
year = {1989},
}

TY - JOUR
AU - Gambaudo, J. M.
AU - Van Strien, S.
AU - Tresser, C.
TI - The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
PB - Gauthier-Villars
VL - 50
IS - 3
SP - 335
EP - 356
LA - eng
KW - periodic orbits; orientation preserving embeddings; zero topology entropy
UR - http://eudml.org/doc/76451
ER -

References

top
  1. REFERENCES [A.F.] D. Asimov and J. Franks, Unremovable Closed Orbits, in Geometric Dynamics, J. PALIS Ed., Lecture Notes in Math., No. 1007, 1983, pp. 22-29, (1983). Zbl0521.58047MR730260
  2. [B. G.L. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young, Periodic Orbits Zbl0447.58028
  3. M.Y.] and Topological Entropy of One-Dimensional Maps, Lecture Notes in Math., No. 819, 1980, pp. 18-34. Zbl0447.58028
  4. [Bi] J. Birman, Braids, Links, and Mapping Class Groups, Annals of Mathematics studies, Princeton University Press, 1975. Zbl0305.57013MR375281
  5. [Bl.F.] P. Blanchard and J. Franks, Dynamical Complexity of Orientation Reversing Diffeomorphisms of Surfaces, Inventiones math., Vol. 62, 1980, pp. 333-339. Zbl0481.58020MR595592
  6. [Bo 1] P. Boyland, Braid Types and a Topological Method of Proving Positive Entropy, preprint, 1987. 
  7. [Bo 2] P. Boyland, An Analog of Sharkovski's. Theorem for Twist Maps, Summer Conference on Hamiltonian Dynamical Systems, proceeding A.M.S.-S.I.A.M. 1987. Zbl0677.58039
  8. [Bro] L.E.J. Brouwer, Über die periodischen transformationen der Kugel, Math. Ann., Vol. 80, 1919, pp. 39-41. Zbl47.0527.01MR1511946JFM47.0527.01
  9. [Ca] A. Casson, Automorphisms of Surfaces After Nielsen and Thurston, lecture notes by S. Bleirer. 
  10. [Ei] S. Eilenberg, Sur les transformations périodiques de la surface de sphere, Fund. Math., Vol. 22, 1934, pp. 28-41. Zbl0008.37109
  11. [F.L.P.] A. Fathi, F. Laudenbach and V. Peanaru, Travaux de Thurston sur les surfaces, Astérisque, Vol. 66-67, 1979. 
  12. [Fr] D. Fried, Entropy and Twisted Cohomology, Topology, Vol. 25, 1986, pp. 455- 470. Zbl0611.58036MR862432
  13. [Ha] M. Handel, Zero Entropy Surface Diffeomorphisms, preprint, 1986. 
  14. [H.W.] P. Holmes and R. Williams, Knotted Periodic Orbits in Suspension of Smale's Horseshoe: Torus Knots and Bifurcation Sequences, Arch. Rat, Mech. Anal., Vol. 90, 1985, pp. 115-194. Zbl0593.58027MR798342
  15. [Ka] A. Katok, Lyapounov Exponents, Entropy and Periodic Orbits for Diffeomorphisms, Publ. Math. I.H.E.S., Vol. 51, 1980, pp. 137-173. Zbl0445.58015MR573822
  16. [Kerc] S.P. Kerckhoff, The Nielsen Realization Problem, Annals of Math., Vol. 117, 1983, pp. 235-265. Zbl0528.57008MR690845
  17. [Kere] B. Kerekjarto, Sur la structure des transformations topologiques des surfaces en elles-mêmes, L'Enseignement Math., Vol. 35, 1936, pp. 297-316. Zbl0016.04403
  18. [Kob] T. Koboyashi, Links of Homeomorphisms of a Disc and Topological Entropy, Invent. math., Vol. 80, 1985, pp. 153-159. Zbl0585.57005MR784534
  19. [Mor] J.W. Morgan, Non-Singular Morse-Smale Flows on 3-Dimensional Manifolds, Topology, Vol. 18, 1978, pp. 41-53. Zbl0406.58020
  20. [Sar] A.N. Sarkovskii, Coexistence of Cycles of a Continuous Map of a Line Into Itself, Ukr. Math., Vol. 16, 1964, pp. 61-71. MR159905
  21. [Smi] J. Smillie, Periodic Points of Surface Homeomorphisms with Zero Entropy, Ergod. Th. & Dynam. Sys., Vol. 3, 1983, pp. 315-334. Zbl0536.58026
  22. [Th] W. Thurston, Three Dimensional Manifolds, Kleinian Groups and Hyperbolic Geometry, Bull. A.M.S., Vol. 6, 1982, pp. 357-381. Zbl0496.57005MR648524

NotesEmbed ?

top

You must be logged in to post comments.