Calculus of Variations and Geometric Measure Theory

The saga of a fish: from a survival guide to closing lemmas for dynamical systems

Eugene Stepanov (St. Petersburg Branch of the Steklov Research Institute of Mathematics of the Russian Academy of Sciences)

created by gelli on 19 Oct 2017

25 oct 2017 -- 18:00   [open in google calendar]

Sala Seminari Dipartimento di Matematica di Pisa


In a recent paper by D. Burago, S. Ivanov and A. Novikov, "A survival guide for feeble fish", it has been shown that a fish with limited velocity capabilities can reach any point in the (possibly unbounded) ocean provided that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This brilliant result substantially extends the celebrated point-to-point controllability theorems (in particular, the one by H. Sussmann and V. Jurdjevic), though being in a sense non constructive. We will give a fish the constructive (or "almost") recipe of how to survive in a turbulent ocean, and show how this is connected to closing lemmas for dynamical systems, in particular to C. Pugh's closing lemma, proving an extension of the latter. Joint work with Sergey Kryzhevich (St. Petersburg and Nova Gorica).