To attain and maintain a top world level in investigations of non-uniformly hyperbolic (chaotic) dynamics in particular low-dimensional (real and complex) in application to celestial mechanics, differential geometry and population dynamics
To develop the holomorphic iteration techniques in meromorphic functions and involve in conformal invariance of scale limits of physical processes (percolation, Ising model)
Fractals vs. chaos. Multifractal spectra
Tame (zero entropy) dynamics, billiards and ergodic theory of flow suspensions of interval exchange maps
