Density of hyperbolicity and tangencies in sectional dissipative regions

Enrique R. Pujals; Martin Sambarino

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1971-2000
  • ISSN: 0294-1449

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Pujals, Enrique R., and Sambarino, Martin. "Density of hyperbolicity and tangencies in sectional dissipative regions." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1971-2000. <http://eudml.org/doc/78921>.

@article{Pujals2009,
author = {Pujals, Enrique R., Sambarino, Martin},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {generic dynamics; partial hyperbolicity; dominated splitting; homoclinic bifurcations; homoclinic tangencies},
language = {eng},
number = {5},
pages = {1971-2000},
publisher = {Elsevier},
title = {Density of hyperbolicity and tangencies in sectional dissipative regions},
url = {http://eudml.org/doc/78921},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Pujals, Enrique R.
AU - Sambarino, Martin
TI - Density of hyperbolicity and tangencies in sectional dissipative regions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1971
EP - 2000
LA - eng
KW - generic dynamics; partial hyperbolicity; dominated splitting; homoclinic bifurcations; homoclinic tangencies
UR - http://eudml.org/doc/78921
ER -

References

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  1. [1] Bowen R., Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer-Verlag, 1975. Zbl0308.28010MR442989
  2. [2] Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math.115 (2000) 157-193. Zbl0996.37033MR1749677
  3. [3] de Melo W., van Strien S., One-Dimensional Dynamics, Springer-Verlag, 1993. Zbl0791.58003MR1239171
  4. [4] Franks J., Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc.158 (1971) 301-308. Zbl0219.58005MR283812
  5. [5] Franks J., Anosov diffeomorphisms, in: Proc. Symp. Pure Math., vol. 14, AMS, Providence, 1970, pp. 133-164. Zbl0207.54304MR271990
  6. [6] Fathi A., Expansiveness, hyperbolicity and Hausdorff dimension, Comm. Math. Phys.126 (2) (1989) 249-262. Zbl0819.58026MR1027497
  7. [7] Hirsch M., Pugh C., Shub M., Invariant Manifolds, Lecture Notes in Math., vol. 583, Springer-Verlag, 1977. Zbl0355.58009MR501173
  8. [8] Mañé R., Ergodic Theory and Differential Dynamics, Springer-Verlag, New York, 1987. Zbl0616.28007MR889254
  9. [9] Mañé R., An ergodic closing lemma, Ann. of Math.116 (1982) 503-540. Zbl0511.58029MR678479
  10. [10] Newhouse S., Non-density of Axiom A(a) on S 2 , Proc. AMS Symp. Pure Math.14 (1970) 191-202. Zbl0206.25801
  11. [11] Newhouse S., Diffeomorphism with infinitely many sinks, Topology13 (1974) 9-18. Zbl0275.58016MR339291
  12. [12] Newhouse S., The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES50 (1979) 101-151. Zbl0445.58022MR556584
  13. [13] Newhouse S., Hyperbolic limit sets, Trans. Amer. Math. Soc.167 (1972) 125-150. Zbl0239.58009MR295388
  14. [14] Palis J., A global view of dynamics and a conjecture on the denseness of finitude of attractors, Astérisque261 (2000) xiii-xiv, 335–347. Zbl1044.37014MR1755446
  15. [15] Palis J., A global perspective for non-conservative dynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (4) (2005) 485-507. Zbl1143.37016MR2145722
  16. [16] Pliss V.A., On a conjecture due to Smale, Diff. Uravnenija8 (1972) 268-282. Zbl0243.34077MR299909
  17. [17] Pujals E., Sambarino M., Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Ann. of Math.151 (3) (2000) 961-1023. Zbl0959.37040MR1779562
  18. [18] Pujals E., Sambarino M., On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy, Nonlinearity13 (2000) 921-926. Zbl0983.37059MR1759008
  19. [19] Pujals E., Sambarino M., Integrability on codimension one dominated splitting, Bull. Braz. Math. Soc. (N.S.)38 (1) (2007) 1-19. Zbl1128.37022MR2302745
  20. [20] Pujals E., Sambarino M., On the dynamics of dominated splitting, Ann. of Math.169 (2009) 675-740. Zbl1178.37032MR2480616
  21. [21] Palis J., Takens F., Hyperbolicity Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Cambridge University Press, 1993. Zbl0790.58014MR1237641
  22. [22] Palis J., Viana M., High dimension diffeomorphisms displaying infinitely many periodic attractors, Ann. of Math. (2)140 (1) (1994) 207-250. Zbl0817.58004MR1289496
  23. [23] Shub M., Global Stability of Dynamical Systems, Springer-Verlag, 1987. Zbl0606.58003MR869255
  24. [24] Wen L., Homoclinic tangencies and dominated splittings, Nonlinearity15 (5) (2002) 1445-1469. Zbl1011.37011MR1925423

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