Homoclinic tangencies and fractal invariants in arbitrary dimension;Tangences homoclines et invariants fractaux en dimension arbitraire

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 333, Issue 5, 2001, Pages 475-480

  Moreira, Carlos Gustavo ^a   Palis, Jacob ^a   Viana, Marcelo ^a  

^a IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041868233     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(01)02085-7     Document Type: Article

References (10)

1. Moreira C.G. Stable intersections of Cantor sets and homoclinic bifurcations. Ann. Inst. Henri-Poincaré, Anal. Non Linéaire. 13:1996;741-781.
2. Moreira C.G., Yoccoz J.-C., Stable intersections of regular Cantor sets with large Hausdorff dimensions, Ann. Math. (to appear).
3. Moreira C.G., Yoccoz J.-C., Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale (in preparation).
4. Newhouse S. The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 50:1979;101-151.
5. Newhouse S., Palis J. Cycles and bifurcation theory. Astérisque. 31:1976;44-140.
6. Palis J., Takens F. Hyperbolicity and the creation of homoclinic orbits. Ann. Math. 125:1987;337-374.
7. Palis J., Takens F. Hyperbolicity and Sensitive Chaotic Dynamics at Homolinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors. 1992;Cambridge Univ. Press.
8. Palis J., Viana M. High dimension diffeomorphisms displaying infinitely many periodic attractors. Ann. Math. 140:1994;207-250.
9. Palis J., Yoccoz J.-C. Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension. Acta Math. 172:1994;91-136.
10. Takens F. Homoclinic bifurcations. Proc. Intern. Congress of Math. 1986;1229-1236 Berkeley.