8th Croatian Mathematical Congress

Statistical properties of random dynamical systems

Not scheduled

20m

Osijek

Plenary lecture DS/ODE: Dynamical Systems, Ordinary Differential Equations and Applications

Speaker

Dr Davor Dragičević (Faculty of Mathematics, University of Rijeka)

Description

We will survey a number of recent results dealing with statistical properties of dynamical systems exhibiting some hyperbolicity. These include various limit theorems (central limit theorem, large deviation principle, almost sure invariance principle etc.) as well as statistical stability and linear response.

References:

[1] D. Dragičević, G. Froyland, C. Gonzalez-Tokman and S. Vaienti, A spectral approach for quenched limit theorems for random expanding dynamical systems, Comm. Math. Phys. 360 (2018), 1121-1187.
[2] D. Dragičević, G. Froyland, C. Gonzalez-Tokman and S. Vaienti, Almost sure invariance principle for random piecewise expanding maps, Nonlinearity 31 (2018), 2252-2280.
[3] D. Dragičević, G. Froyland, C. Gonzalez-Tokman and S. Vaienti, A spectral approach for quenched limit theorems for random hyperbolic dynamical systems, Trans. Amer. Math. Soc. 373 (2020), 629-664.
[4] D. Dragičević and Y. Hafouta, Almost sure invariance principle for random dynamical systems via Gouëzel's approach, Nonlinearity 34 (2021), 6773-6798.
[5] D. Dragičević and J. Sedro, Statistical stability and linear response for random hyperbolic dynamics, Ergodic Theory Dynam. Systems 43 (2023), 515-544.
[6] D. Dragičević, Y. Hafouta and J. Sedro, A vector-valued almost sure invariance principle for random expanding on average cocycles, J. Stat. Phys. 190 (2023), 38pp.
[7] D. Dragičević, P. Giulietti and J. Sedro, Quenched linear response for smooth expanding on average cocycles, Comm. Math. Phys. 399 (2023), 423-452.
[8] D. Dragičević and Y. Hafouta, Effective quenched linear response for random dynamical systems, in preparation.