منابع مشابه
Hyperbolicity of General Deformations
This is the content of the talk given at the conference “Effective Aspects of Complex Hyperbolic Varieties”, Aver Wrac’h, France, September 10-14, 07. We present two methods of constructing low degree Kobayashi hyperbolic hypersurfaces in Pn: • The projection method • The deformation method The talk is based on joint works of the speaker with B. Shiffman and C. Ciliberto. 1. DIGEST on KOBAYASHI...
متن کاملHyperbolicity of General Deformations: Proofs
We modify the deformation method from [9] in order to construct further examples of Kobayashi hyperbolic surfaces in P of any even degree d ≥ 8. Given a hypersurface Xd = f ∗ d (0) in P n of degree d, we say that a (very) general small deformation of Xd is hyperbolic if for any (very) general degree d hypersurface X∞ = g ∗ d(0) and for all sufficiently small ε ∈ C \ {0} (depending on X∞) the hy...
متن کاملGeneric hyperbolicity of Aubry sets on surfaces
Given a Tonelli Hamiltonian of class C on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the C topology for which the Aubry set is hyperbolic in its energy level.
متن کاملUniform (projective) Hyperbolicity or No Hyperbolicity: a Dichotomy for Generic Conservative Maps
– We show that the Lyapunov exponents of volume preserving C1 diffeomorphisms of a compact manifold are continuous at a given diffeomorphism if and only if the Oseledets splitting is either dominated or trivial. It follows that for a C1-residual subset of volume preserving diffeomorphisms the Oseledets splitting is either dominated or trivial. We obtain analogous results in the setting of sympl...
متن کاملNew Criteria of Generic Hyperbolicity Based on Periodic Points
We prove that, if a mild condition on the hyperbolicity of the periodic points holds for any diffeomorphism in a residual subset of a C-open set U , then such set U exhibits a residual subset A of Axiom A diffeomorphisms. We also prove an analogous result for nonsingular endomorphisms: if a mild expanding condition holds for the periodic set of local diffeomorphisms belonging in a residual subs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Functional Analysis and Its Applications
سال: 2009
ISSN: 0016-2663,1573-8485
DOI: 10.1007/s10688-009-0015-0