arXiv subjects
Publications and source records attributed to Dmitry Todorov.
It is proved that bounded solutions of modified ($θ$-twisted) cohomological equations for expanding circle maps are $θ$-Hölder continuous but are not $(θ+γ)$-Hölder continuous for every $γ>0$ at almost every point. This gives new examples of "nonlinear" Weierstrass-like functions for which the optimal \holder exponent at most points is known.
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
We prove that Lipschitz inverse shadowing for nonsingular flows is equivalent to structural stability.
We generalize two classical results of Maizel and Pliss that describe relations between hyperbolicity properties of linear system of difference equations and its ability to have a bounded solution for every bounded inhomogeneity. We also apply one of this generalizations in shadowing theory of diffeomorphisms to prove that some sort of limit shadowing is equivalent to structural stability.
We prove that spaces of Keplerian curvilinear orbits, all orbits and elliptic orbits with marked pericenter cannot carry a norm, compatible with their standard topology. We also prove that the space of Keplerian elliptic orbits without marked pericenter cannot carry a norm, compatible with the natural metrics on it.