Periodic points and homoclinic classes

By F. Abdenur, C. Bonatti, S. Crovisier, Lorenzo Justiniano Díaz Casado, Lan Wen. Ergodic Theory and Dynamical Systems, 2006

95 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c0d39b07d082664a2bb97a07e2df43b802fb82e9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. S. Crovisier
2. C. Bonatti
3. Lorenzo J. Díaz
4. E. Pujals
5. F. Abdenur
6. Marcelo Viana
7. Artur Avila
8. Jiagang Yang

In Mathematical Physics

1. S. Crovisier
2. C. Bonatti
3. Lorenzo J. Díaz
4. E. Pujals
5. F. Abdenur
6. Marcelo Viana
7. Jiagang Yang
8. Shaobo Gan

In Statistical and Nonlinear Physics

1. S. Crovisier
2. C. Bonatti
3. Lorenzo J. Díaz
4. F. Abdenur
5. E. Pujals
6. Marcelo Viana
7. Jiagang Yang
8. Artur Avila

Citations in the corpus

• Abundance of C 1 -robust homoclinic tangencies (2009, background): “Let us observe that, for an open and dense subset of T (M), a chain recurrence class is either hyperbolic or has index variation, see [2].”
• Nonuniform hyperbolicity for C1-generic diffeomorphisms (2008, methodology): “It turns out, however, that many of these tools { especially from [ ABCDW ], [BDP], and [BDPR] { are also useful for the study of generic ergodic problems.”
• Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms (2010, background): “From the results in [2] follows that H(p) contains periodic orbits whose center exponents are arbitrarily close to 0.”
• Partial hyperbolicity far from homoclinic bifurcations (2008, background): “non-empty transverse intersection (see [ ABCDW , lemma 2.9]).”
• ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS (2007, background): “For an explicit formulation of this result (and its complete proof) see [ ABCDW , Lemma 2.1].”