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

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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

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  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

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