Hamiltonian Systems and Liouville Integrability

[qspeechc]

Hi

I am a mathematics junior and I am doing a research project on hamiltonian systems and liouville integrability (don't ask why...). I am using the book by Vilasi, a graduate level book, but I am finding it quite difficult and badly written; for instance he uses functional analysis and differential geometry concepts without defining things, explaining or proving certain things. He also expects you o already know Hamiltonian dynamics. So I was wondering if there is a relatively simple book that would cover Liouville integrability (NOT Liouville's theorem as given "[URL for phase space)? By relatively simple, I mean ofcourse accessible to me, a junior math student (all the physics I once knew I have mostly forgotten, but I am using Goldstein to help me along the way).

 

[qspeechc]

I guess this means no one can help me?

 

[sir-pinski]

Hello there,

I completely understand your frustration with the book you are using for your research project. It can be challenging to find a good resource that explains complex mathematical concepts in a clear and accessible way. However, I believe there are a few options you can explore to help you better understand Hamiltonian systems and Liouville integrability.

First, I would recommend checking out some online resources such as lecture notes or video lectures on these topics. There are many universities that offer open access to their course materials, and you may be able to find some helpful resources there. Additionally, there are also online forums and discussion groups where you can ask questions and get help from other students or experts in the field.

Secondly, you can also try looking for other books on the subject that may be more suitable for your level of understanding. A few recommendations that I have are "Hamiltonian Dynamics" by John Hubbard and Beverly West, "Classical Mechanics: Point Particles and Relativity" by Walter Greiner, and "Introduction to Hamiltonian Dynamical Systems and the N-Body Problem" by Kenneth R. Meyer and Glen R. Hall. These books are written at a more introductory level and may provide a better foundation for understanding Hamiltonian systems and Liouville integrability.

Lastly, don't be afraid to reach out to your professor or a math tutor for additional help and guidance. They may be able to offer some additional resources or explanations that can help clarify any confusion you may have.

I hope these suggestions are helpful and wish you the best of luck with your research project!