3 papers
math.DS2025
Generalized hyperbolicity for diffeomorphisms of Banach spaces
Sergey Tikhomirov
We introduce generalized hyperbolicity for nonlinear dynamics in Banach spaces. The definition allows the stable/unstable splitting to be discontinuous and requires only inclusions…
math.AP2024
Properties of the phase boundary in the parabolic problem with hysteresis
Darya Apushkinskaya, Sergey Tikhomirov, Nina Uraltseva
We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial…
math.DS2024
Probabilistic shadowing in linear skew products
Grigorii Monakov, Sergey Tikhomirov
We investigate the probability of shadowing of a random finite pseudotrajectory by an exact trajectory for linear skew products. We describe general conditions under which a random…