Qualitative Theory Of Odes: An Introduction To Dynamical Systems Theory
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A01=Henryk Zoladek
A01=Raul Murillo
Author_Henryk Zoladek
Author_Raul Murillo
Averaging in Differential Equations
Bifurcations of Vector Fields
Category=PBKJ
Chaotic Dynamics
eq_isMigrated=1
eq_nobargain
Ergodic Properties of Differential Equations
Hyperbolic Dynamics
Integrability in Hamiltonian Mechanics
Kam Theory
Phase Portraits of Vector Fields
Quasi-Periodic Motion
Slow-Fast Systems
Smale Horseshoe
Stability
Structural Stability
Product details
- ISBN 9781800612686
- Publication Date: 19 Dec 2022
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state.Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on Raul Murillo's translation of Henryk Żołądek's lecture notes, which were in Polish and edited in the portal Matematyka Stosowana (Applied Mathematics) in the University of Warsaw.
