Related papers: Linearization of quasiperiodically forced circle f…
In this article we show a $C^{0,\alpha}$-partial regularity result for solutions of a certain class of cross-diffusion systems with entropy structure. Under slightly more stringent conditions on the system, we are able to obtain a…
The liftable centralizer for special flows over irrational rotations is studied. It is shown that there are such flows under piecewise constant roof functions which are rigid and whose liftable centralizer is trivial.
We consider the reducibility problem of cocycles $(\alpha,A)$ on $\T^d\times U(n)$ in Gevrey classes, where $ \alpha$ is a Diophantine vector. We prove that, if a Gevrey cocycle is conjugated to a constant cocycle $(\alpha,C)$ by a suitable…
We study the circle homeomorphisms extensions over a strictly ergodic homeomorphism. Under a very mild restriction, we show that the fibered rotation number is locally constant on an open and dense subset. In the complement of this set, we…
The rigidity theory for circle homeomophisms with breaks was studied intensively in the last 20 years. It was proved that under mild conditions of the Diophantine type on the rotation number any two $C^{2+\alpha}$ smooth circle…
We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…
Considered herein is the reducibility of the quasi-periodically time dependent linear dynamical system with a diophantine frequency vector $\omega \in \mathcal{O}_0 \subset \mathbb{R}^{\nu}$. This system is derived from linearizing the…
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result…
We define a measurable spin for the edge of a lowest Landau level and incompressible fractional quantum Hall state in the presence of an Abelian or non-Abelian bulk quasiparticle. We show that this quantity takes a fractional value…
We study a large class of suspension semiflows which contains the Lorenz semiflows. This is a class with low regularity (merely C^{1+\alpha}) and where the return map is discontinuous and the return time is unbounded. We establish the…
We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show that conditional on the velocity field, the quenched…
We propose that stretched horizons can be described in terms of a gas of non-interacting quasiparticles. The quasiparticles are unstable, with a lifetime set by the imaginary part of the lowest quasinormal mode frequency. If the horizon…
Given a continuous family of C^2 functionals of Fredholm type, we show that the non-vanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial…
For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact"…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence…
The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…
This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant…