Resources and guides about Perturbation theory

In summary, Gal is looking for resources on the classic Perturbation Theory, specifically methods to transform singular problems to regular problems and more advanced techniques like the two scale method. One recommended resource is "Perturbation theory of dynamical systems" with a helpful introductory chapter.
  • #1
The-herod
24
0
Hello,

I have to learn about the classic Perturbation Theory.
I'm looking for guides, textbooks etc about Perturbation Theory. I already know the basis (Poincare method), but I found it hard to find resources for more advanced material on the one hand, that will also teach it from basis on the other. I'm trying to focus now on methods to transform of singular problems to regular problems, and more advanced methods (like the two scale method).

I'll really appreciate any help and so. I'm pretty stuck now...

Thanks a lot!
Gal
 
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  • #2
You might have a look at "Perturbation theory of dynamical systems" http://arxiv.org/abs/math/0111178

The first introductory chapter is quite nice, but the other chapters are very mathematical and very frightening :eek: (at least for a hobby-physicist like me, maybe for you they are useful).
 
  • #3
Great, I'll have a look at this now.

Thanks!:smile:
 

What is perturbation theory?

Perturbation theory is a mathematical method used to approximate solutions to problems that cannot be solved exactly. It is commonly used in physics and engineering to solve problems involving small changes or disturbances from a known or idealized system.

How does perturbation theory work?

Perturbation theory works by breaking down a complex system into a simpler, known system, and then using mathematical techniques to incorporate the effects of the perturbation on the known system. The result is an approximate solution that can be used to understand the behavior of the original system.

What are the benefits of using perturbation theory?

Perturbation theory allows scientists and engineers to solve problems that would otherwise be too difficult or impossible to solve. It also provides a deeper understanding of the behavior of complex systems and can be used to make predictions about their future behavior.

What are the limitations of perturbation theory?

Perturbation theory is only effective for small perturbations from a known system. If the perturbation is too large, the results may not be accurate. In addition, perturbation theory may not work for highly nonlinear systems or systems with chaotic behavior.

How is perturbation theory applied in different fields of science?

Perturbation theory is used in a variety of fields, including physics, chemistry, engineering, and economics. In physics, it is used to study the behavior of particles in quantum mechanics and the motion of celestial bodies in astrophysics. In chemistry, it is used to understand the behavior of molecules and chemical reactions. In engineering, it is used to design and analyze complex systems. In economics, it is used to model changes in market conditions and predict economic outcomes.

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