48 citations · 178 across the 24 of their papers we have counts for
17 papers · 1 filter
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…
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 absolute nonshadowability of transitive maps
Sergey Tikhomirov
We study shadowing property for random infinite pseudotrajectories of a continuous map of a compact metric space. For the cases of transitive maps and transitive attractors we…
Nonlocally maximal and premaximal hyperbolic sets
T. Fisher, T. Petty, S. Tikhomirov
We prove that for any closed manifold of dimension 3 or greater that there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one.…
Shadowing in linear skew products
Sergey Tikhomirov
We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typic…