11:30 - 12:15 - Carlos H. Vasquez (PUC, Valparaiso)

Differentiability of Lyapunov Exponents

In this work, we consider a C^∞- one parameter family of C^r, r≥1, diffeomorphisms f_t,t∈I, defined on a compact orientable Riemannian manifold M. If the family admits a continuous 〖Df〗_t-invariant subbundle E(t,⋅) and an invariant probability measure μ for every t∈I, then the integrated Lyapunov exponent λ(t) of f_t over E(t) is well defined. We discuss about conditions for the differentiability of λ(t) in t=0.
This a work in progress joint with Radu Saghin and Pancho Valenzuela-Henríquez.

14:00 - 14:45 - Sergey Kryzhevich (University of Nova Gorica)

Partial Hyperbolicity and Central Shadowing

This is a joint work with Sergey Tikhomirov. We consider partially hyperbolic diffeomorphisms of compact manifolds. Suppose that the so-called dynamical coherence condition is satisfied: central stable and central unstable bundles are uniquely integrable. We demonstrate that the considered dynamical system has the central shadowing property: for any pseudotrajectory there exists a close one where all errors are small shifts along the central foliation. Also, some corollaries to the theory to Dynamical Systems and Geometry and farther development of the approach will be discussed.

15:00 - 15:45 - Tarakanta Nayak (IIT Bhubaneswar)

Completely invariant domains

Given a meromorphic function from the Riemann sphere to itself, a domain is called completely invariant if its image and the pre-image under the function are contained in itself. The talk deals with completely invariant domains and its implications in complex dynamics. It is conjectured that the number of completely invariant domains for every meromorphic function is at most two. The status of this conjecture and some related work are to be presented.