On evolution of small spheres in the phase space of a dynamical system*
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.
On exactness of upper estimates of the characteristic exponent of a linear system with exponentially decreasing perturbations.
On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore,...
On the decay rate of solutions of non-autonomous differential systems.
On the definition of strange nonchaotic attractor
The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove that a whole...
On the enumerable set of different characteristic sets of solutions of a Pfaffian linear system.
On the existence of a measure unbounded exponential spectral characteristic set of a linear system with a small parameter at the derivative.
On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the stability of solutions to a class of nonlinear difference systems.
Oб инвариантности характеристических показателей линейных систем при экспоненциально убывающих возмущениях