Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
GA Leonov, VA Boichenko - Acta Applicandae Mathematica, 1992 - Springer
This paper surveys results of the authors and others conceming estimates for the Hausdorff
dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and …
dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and …
[图书][B] Attractors for equations of mathematical physics
VV Chepyzhov, MI Vishik - 2002 - books.google.com
One of the major problems in the study of evolution equations of mathematical physics is the
investigation of the behavior of the solutions to these equations when time is large or tends …
investigation of the behavior of the solutions to these equations when time is large or tends …
[图书][B] Navier-Stokes equations and turbulence
C Foias, O Manley, R Rosa, R Temam - 2001 - books.google.com
This book aims to bridge the gap between practising mathematicians and the practitioners of
turbulence theory. It presents the mathematical theory of turbulence to engineers and …
turbulence theory. It presents the mathematical theory of turbulence to engineers and …
[图书][B] Weak and measure-valued solutions to evolutionary PDEs
Weak and Measure-valued Solutions to Evolutionary PDEs Page 1 Weak and Measure-valued
Solutions to Evolutionary PDEs Page 2 APPLIED MATHEMATICS AND MATHEMATICAL …
Solutions to Evolutionary PDEs Page 2 APPLIED MATHEMATICS AND MATHEMATICAL …
[HTML][HTML] The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension
On the example of the famous Lorenz system, the difficulties and opportunities of reliable
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …
[图书][B] Applied analysis of the Navier-Stokes equations
CR Doering, JD Gibbon - 1995 - books.google.com
The Navier-Stokes equations are a set of nonlinear partial differential equations that
describe the fundamental dynamics of fluid motion. They are applied routinely to problems in …
describe the fundamental dynamics of fluid motion. They are applied routinely to problems in …
[PDF][PDF] Global attractors in partial differential equations
G Raugel - Handbook of dynamical systems, 2002 - imo.universite-paris-saclay.fr
This survey is devoted to an introduction to the theory of global attractors for semigroups
defined on infinite dimensional spaces, which has mainly been developed in the last three …
defined on infinite dimensional spaces, which has mainly been developed in the last three …
[图书][B] Attractor dimension estimates for dynamical systems: theory and computation
N Kuznetsov, V Reitmann - 2020 - Springer
In this book, we continue the investigations of global attractors and invariant sets for
dynamical systems by means of Lyapunov functions and adapted metrics. The effectiveness …
dynamical systems by means of Lyapunov functions and adapted metrics. The effectiveness …
[HTML][HTML] The Lyapunov dimension and its estimation via the Leonov method
NV Kuznetsov - Physics Letters A, 2016 - Elsevier
Along with widely used numerical methods for estimating and computing the Lyapunov
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …
dimension there is an effective analytical approach, proposed by GA Leonov in 1991. The …
On RA Smith's autonomous convergence theorem
MY Li, JS Muldowney - The Rocky Mountain Journal of Mathematics, 1995 - JSTOR
RA Smith [19] showed that his higher dimensional generalization of Bendixson's criterion for
the nonexistence of periodic solutions to an autonomous differential equation implies that all …
the nonexistence of periodic solutions to an autonomous differential equation implies that all …