Dynamics of Quasi-Stable Dissipative Systems by Igor Chueshov

By Igor Chueshov

This ebook is dedicated to heritage fabric and lately constructed mathematical equipment within the examine of infinite-dimensional dissipative structures. the speculation of such structures is encouraged via the long term target to set up rigorous mathematical types for turbulent and chaotic phenomena. the purpose here's to provide normal tools and summary effects bearing on basic dynamical platforms homes relating to dissipative long-time habit. The ebook systematically provides, develops and makes use of the quasi-stability procedure whereas considerably extending it by means of together with for attention new periods of versions and PDE structures bobbing up in Continuum Mechanics. The ebook can be utilized as a textbook in dissipative dynamics on the graduate level.

Igor Chueshov is a Professor of arithmetic at Karazin Kharkov nationwide college in Kharkov, Ukraine.

Show description

Read Online or Download Dynamics of Quasi-Stable Dissipative Systems PDF

Similar mathematical physics books

An Introduction to Chaos in Nonequilibrium Statistical Mechanics

This publication is an creation to the functions in nonequilibrium statistical mechanics of chaotic dynamics, and likewise to using thoughts in statistical mechanics vital for an knowing of the chaotic behaviour of fluid platforms. the elemental techniques of dynamical structures thought are reviewed and straightforward examples are given.

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

"José Ferreirós has written a magisterial account of the historical past of set idea that is panoramic, balanced, and interesting. not just does this e-book synthesize a lot earlier paintings and supply clean insights and issues of view, however it additionally contains a significant innovation, a full-fledged therapy of the emergence of the set-theoretic technique in arithmetic from the early 19th century.

Computational Physics: Problem Solving with Python

Using computation and simulation has turn into a vital a part of the clinical procedure. with the ability to rework a conception into an set of rules calls for major theoretical perception, particular actual and mathematical realizing, and a operating point of competency in programming. This upper-division textual content offers an strangely wide survey of the subjects of recent computational physics from a multidisciplinary, computational technology viewpoint.

Extra resources for Dynamics of Quasi-Stable Dissipative Systems

Sample text

15. 0/ D 0. In relation to this example, it is interesting to mention the following simple assertion concerning uniqueness for 1D equations. 16. Let f W R 7! R be a continuous function. x0 / ¤ 0. Proof. 2 in the Appendix). The same theorem yields the uniqueness in the Lipschitz case. x0 / ¤ 0 only. x/ is continuous and preserves the sign. x/ D dt Z x x0 d : f. t// D t for all t > 0 small enough. t/ is locally unique. 17. 15 is locally unique for every initial datum x0 ¤ 0. t/ outside a small neighborhood of this x0 is also unique.

6, v is a Lyapunov stable fixed point. v; w/ Ä ı. St w/ ! 0 as t ! C1. 3 yields that St w ! 0. Hence, v is asymptotically Lyapunov stable. 7 Complete theory of 1D continuous systems Now we describe all possible scenarios in one-dimensional systems with continuous time. We start with several simple observations by including them in the following exercises. 1. Describe the dynamics in the models generated by the following equations: (a) xP D x, (b) xP D x, (c) xP D jxj, (d) xP D 1. Show that the corresponding dynamical systems cannot be topologically equivalent.

X/ for all x; t 2 R: We also have the following assertion. 10. R; St / with continuous reversible time is conjugate with a system generated by some ordinary differential equation. Proof. We use the argument given in SIBIRSKY [212]. x/ D 0 for every x 2 N . a; b/: We perform this similarly in the case b D 1. x/ generates a dynamical system with continuous reversible time. St ; R/. t u We do not know whether a similar result holds in higher dimensions. 11. R; SQ t / with reversible time have finite numbers of equilibria N D fx1 < x2 < : : : < xN g and NQ D fQx1 < xQ 2 < : : : < xQ NQ g: D C1.

Download PDF sample

Rated 4.54 of 5 – based on 11 votes