We prove the hyperbolicity of the complement of five lines in general position in an almost complex projective plane, answering a question by S. Ivashkovich.

In this brief note, it is shown that the random hyperbolicity of a random linear cocycle is equivalent to having the Lipschitz shadowing property.

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic 6= 2 remains non-hyperbolic over some splitting field of the algebra.

Let A be a finite dimensional Q-algebra and Γ ⊂ A a Z-order. We classify those A with the property that Z 6 →֒U(Γ). We call this last property the hyperbolic property. We apply this in the case that A = KS a semigroup algebra with K = Q or K = Q( √ −d). In particular, when KS is semi-simple and has no nilpotent elements, we prove that S is an inverse semigroup which is the disjoint union of Higm...

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...

We show that a nodal hypersurface X in P3 of degree d with a sufficiently large number l of nodes, l > 8 3 (d2 − 5 2 d), is algebraically quasi-hyperbolic, i.e. X can only have finitely many rational and elliptic curves. Our results use the theory of symmetric differentials and algebraic foliations and give a very striking example of the jumping of the number of symmetric differentials in famil...

A complex manifold X is said to be hyperbolic (in the sense of Brody) if every analytic map from the complex plane C to X is constant. From Picard’s “little” theorem, an entire function missing more than two values must be constant. It is equivalent to say that P \ {0, 1,∞} is hyperbolic. Picard’s theorem also show that a Riemann surface of genus one omitting one point and Riemann surfaces of g...

We show that the property of admitting a coarse median structure is preserved under relative hyperbolicity for finitely generated groups. 2010 Mathematics Subject Classification : 20F65

We consider a class of Hamiltonian systems with elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.