PANDA (Patterns, Nonlinear Dynamics and Applications)

Tuesday 3 June 2014

Department of Mathematical Sciences

University of Bath

Ivan Ovsyannikov (Imperial)

An analytic proof of Lorenz-like attractors in continuous and discrete time models

 
Abstract: The Lorenz system was the first natural model exhibiting chaotic dynamics. But there was no analytical proof of existence of the Lorenz attractor in the Lorenz system (the 14th Smale's problem). The only known proof proposed by Tucker was computer-assisted. My recent results provide a theoretical (non computer-assisted) proof for the Lorenz-Yudovich model using the Shilnikov criterion. These results are useful also for the proof of the birth of discrete Lorenz attractors in local and global bifurcations of diffeomorphisms.