Hamiltonian Systems and Liouville Integrability

Click For Summary
SUMMARY

The discussion centers on the challenges faced by a mathematics junior studying Hamiltonian systems and Liouville integrability, particularly using Vilasi's graduate-level book, which lacks clarity and foundational explanations. The participant seeks recommendations for simpler resources that specifically address Liouville integrability without delving into Liouville's theorem. They mention using Goldstein's work as supplementary material to aid their understanding of Hamiltonian dynamics.

PREREQUISITES
  • Understanding of Hamiltonian dynamics
  • Familiarity with functional analysis concepts
  • Basic knowledge of differential geometry
  • Access to graduate-level mathematics resources
NEXT STEPS
  • Research alternative textbooks on Liouville integrability, focusing on accessibility for undergraduates
  • Explore introductory materials on Hamiltonian dynamics, such as "Classical Mechanics" by Goldstein
  • Investigate online courses or lectures covering functional analysis and differential geometry
  • Look for forums or study groups focused on Hamiltonian systems for peer support
USEFUL FOR

Mathematics students, particularly those in undergraduate programs, researchers in dynamical systems, and anyone seeking to understand Hamiltonian systems and Liouville integrability in a more accessible manner.

qspeechc
Messages
839
Reaction score
15
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).
 
Last edited by a moderator:
Physics news on Phys.org
I guess this means no one can help me?
 

Similar threads

Graduate Spectrum of the Liouville Operator
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Boltzmann equation and Hamiltonian
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Does Noether's Theorem Extend Beyond Conservation in Hamiltonian Systems?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Is any Hamiltonian system integrable?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Energy in the Hamiltonian formalism from phase space evolution
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Integrability of the tautological 1-form
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Solving this non-holonomic system using Dirac-Bergmann theory
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Challenging Susskind's uncompressible flow in Liouville’s Theorem
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Question on derivation of a property of Poisson brackets
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Liouville's theorem and time evolution of ensemble average
  • · Replies 2 ·
Replies
2
Views
3K