Since the early part of the 20th century, it has been understood that the description of nature
at the subatomic scale requires quantum mechanics. In quantum mechanics, the position …

Grzegorz Łukaszewicz Piotr Kalita An Introduction with Applications Page 1 Advances in
Mechanics and Mathematics 34 Grzegorz Łukaszewicz Piotr Kalita Navier– Stokes …

This paper is devoted to establishing a (random) uniform attractor theory for non-
autonomous random dynamical systems (NRDS). The uniform attractor is defined as the …

The theories of nonautonomous and random dynamical systems have undergone extensive,
often parallel, developments in the past two decades. In particular, new concepts of …

Nonautonomous oscillatory systems with stable amplitudes and time-varying frequencies
have often been treated as stochastic, inappropriately. We therefore formulate them as a …

Autonomous systems depend only on the elapsed time, so their attractors and limit sets exist
in current time. Similarly, the pullback limit defines a component set of a nonautonomous …

Forward attractors, especially invariant ones, of non-autonomous and random dynamical
systems have not been as well studied as pullback attractors. This is mainly due to the …

The celebrated Takens' embedding theorem concerns embedding an attractor of a
dynamical system in a Euclidean space of appropriate dimension through a generic delay …

A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given
input sequence, it “forgets” any internal states of the driven (nonautonomous) system and …

In this work, we establish several criteria for the existence as well as the upper semi-
continuity of bi-spatial attractors under a closedness condition, which dramatically weakens …