Predavatelj: Jan Boroński (AGH University of Science and Technology)
I will present my joint work with Sonja Štimac on classification of strange attractors. Among the many results, our work relies on the notion of mild dissipation [CP], which allows for an inverse limit description, in terms of densely branching trees [BS].
For a large family of attractors, that include those of Lozi and Henon, two strange attractors are equivalent if and only if their kneading sequences coincide, if and only if their folding patterns agree.
[BC] M. Benedicks, L.A.E. Carleson, The dynamics of the Henon map, Annals of Mathematics 133 (1991), 73–169.
[BS] J. Boroński, S. Štimac, Densely branching trees as models for Henon-like and Lozi-like attractors, preprint 2021, arXiv:2104.14780
[CP] S. Crovisier, E. Pujals, Strongly dissipative surface diffeomorphisms, Commentarii Mathematici Helvetici 93 (2018), 377–400.
[MS] M. Misiurewicz, S. Štimac, Symbolic dynamics for Lozi maps, Nonlinearity 29 (2016), 3031–3046.
[WY] Wang, Q.; Young, L.-S. Strange attractors with one direction of instability. Comm. Math. Phys. 218 (2001), 1–97.