48 citations · 178 across the 24 of their papers we have counts for
27 papers
Discontinuous Generalized Hyperbolicity and Structural Stability
Sergey Tikhomirov
We study diffeomorphisms of Banach spaces satisfying generalized hyperbolicity: the stable and unstable subspaces are invariant only up to inclusion, need not depend continuously o…
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…
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…
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…
On displacement of viscous liquid in a system of parallel tubes
Grigorii V. Monakov, Sergey B. Tikhomirov, Andrey A. Yakovlev
An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stabili…
Error estimates for Riemann sums of some singular functions
Pavel Gurevich, Sergey Tikhomirov
In this short note, we obtain error estimates for Riemann sums of some singular functions.