ICTP Mathematics Seminar - Tuesday 27 June (please note change of schedule: Vasquez/Nayak)

[Math Group]

M A T H E M A T I C S   S E M I N A R S 2017


Tuesday, 27 June, starting at 11:30 hrs.


Venue: ICTP Stasi seminar room


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.


-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy

Tel. no.: +39-040-2240455
math at ictp.it
http://math.ictp.it