On the -stability conjecture
Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for smooth, meaning C ∞, parametrized families {g t ∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic) horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative speed as...
Bifurcations and global stability of families of gradients
Bifurcations and stability of families of diffeomorphisms
The topology of holomorphic flows with singularity
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