Citations
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Book ChapterDOI
Infinite dimensional dynamical systems
TL;DR: In this paper, an approach for the discussion of the qualitative theory of infinite dimensional dynamical systems is outlined for the analysis of finite-dimensional systems, and the use of functional differential equations is used to illustrate the usefulness of the approach and the limitations of our present knowledge.
Journal ArticleDOI
Chaotic attractors of an infinite-dimensional dynamical system
TL;DR: In this paper, the chaotic attractors of a delay differential equation were studied and the dimension of several attractors computed directly from the definition agreed to experimental resolution with the dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke.
Book
Long-time Behavior of Second Order Evolution Equations With Nonlinear Damping
Igor Chueshov,Irena Lasiecka +1 more
TL;DR: In this paper, the existence of compact global attractors for evolutions of the second order in time was studied for the Semilinear wave equation with a nonlinear dissipation Von Karman evolutions and other models from continuum mechanics.
Journal ArticleDOI
Three distinct modes in a cold atmospheric pressure plasma jet
TL;DR: In this paper, it is shown that immediately following breakdown, the plasma jet operates in a deterministic chaotic mode, and with increasing input power, the discharge becomes periodic and the jet plasma is found to produce at least one strong plasma bullet every cycle of the applied voltage.
References
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Journal ArticleDOI
A mathematical example displaying features of turbulence
TL;DR: In this paper, the authors consider an incompressible and homogeneous viscous fluid within given material boundaries under given exterior forces and assume that the boundary conditions and the outside forces are stationary, i.e. independent of time.
Book
Properties of Solutions of Ordinary Differential Equations in Banach Space
S. Agmon,Louis Nirenberg +1 more
TL;DR: In this article, the authors studied the behavior of solutions of Lu = 1 dui dt - Au = 0 for functions u(t) with values in some Banach space, as well as inhomogeneous equations Lu = f and ligh ly perturbed equations, with the main emphasis on the behaviour of solutions a t +.
Journal ArticleDOI
Some modern problems in the qualitative theory of ordinary differential equations
TL;DR: In this paper, the authors investigate plane systems, rough systems and rough systems on the surface of a torus, convergence and stability in the large and periodic solutions in many-dimensional systems.
Journal ArticleDOI
Asymptotic decay of solutions of differential inequalities.
Paul J. Cohen,Milton Lees +1 more