Hyperbolicity of a special one-parameter family with a first homoclinic tangency

Dynamical Systems

Volumn 11, Issue 1, 1996, Pages 03-18

  Kiriki, Shin ^a  

^a TOKYO DENKI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); PARAMETER ESTIMATION; PROBLEM SOLVING;

FIRST BIFURCATION; FIRST HOMOCLINIC TANGENCY; ONE PARAMETER FAMILIES; PLANAR DIFFEOMORPHISMS; SMALE'S HORSESHOE DIFFEOMORPHISM;

SYSTEM STABILITY;

EID: 0030110681     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119608806214     Document Type: Article

References (9)

1. Hirsch, M., Pugh, C. and Shub, M. (1977) Invariant manifolds. Lecture Nates in Mathematics 583 (Springer, Berlin).
2. Kiriki, S. (1996) The Palis and Takens' problem on the first homoclinic tangency inside the horseshoe. International Journal of Bifurcation and Chaos 6 (in press).
3. Kiriki, S. (1996) The first homoclinic tangency inside the horseshoe with small factual dimensions (in press).
4. Newhouse, S. and Palis, J. (1976) Cycles and bifurcation theory. Astérisque 31, 44-140.
5. Palis, J. and Takens, F. (1985) Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms. Inventiones Math. 82, 397-422.
6. Palis, J. and Takens, F. (1987) Hyperbolicity and the creation of homoclinic orbits. Annals of Mathematics 125, 337-374.
7. Palis, J. and Takens, F. (1993) Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations (Cambridge University Press, Cambridge).
8. Smale, S. (1965) Diffeomorphisms with many periodic points. Differential Combinatorial Topology (Princeton University Press, Princeton, NJ), pp. 63-80.
9. Yang, Z. (1995) Hénon-like maps before or at the first tangency, PhD thesis.