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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.