Hamiltonian systems, integrability, chaos and MATH

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SUMMARY

This discussion centers on the study of Hamiltonian systems, focusing on integrable and non-integrable systems, as well as chaos theory. The participants highlight the complexity of V.I. Arnold's "Mathematical Methods of Classical Mechanics" as a challenging resource for understanding these concepts. They agree that mastering the material may require significant time, with suggestions to explore alternative resources like "Chaos in Dynamical Systems" by Edward Ott for foundational knowledge. The consensus emphasizes the importance of patience and gradual learning in this intricate field of mathematics.

PREREQUISITES
  • Understanding of Hamiltonian mechanics
  • Familiarity with chaos theory
  • Knowledge of dynamical systems
  • Basic mathematical proficiency in differential equations
NEXT STEPS
  • Read "Chaos in Dynamical Systems" by Edward Ott for foundational concepts
  • Study the symplectic structure of Hamilton's equations
  • Explore integrability conditions in Hamiltonian systems
  • Investigate the concept of destroyed tori in chaotic systems
USEFUL FOR

Mathematicians, physicists, and students interested in advanced dynamics, particularly those focusing on Hamiltonian systems and chaos theory.

diegzumillo
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Hi there,

My objective is to study Hamiltonian systems, integrable and non integrable systems, where there will be chaos, etc. I have a general idea of everything.. the destroyed tori, the symplectic structure of hamilton's equations, etc. But nothing is very clear to me! And the most frustrating part of all this is that everything I want to know seems to be described in rich details in this book: V.I. Arnold - Mathematical Methods of Classical Mechanics. But I don't think it's written in any terrestrial language. :confused:

Is there a other way to approach this subject? Don't get me wrong, I love math but to master this book's content I would need a whole year, if not more, probably.

Diego
 
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Diego Floor said:
Don't get me wrong, I love math but to master this book's content I would need a whole year, if not more, probably.

Which is a very reasonable amount of time for this subject. If you try to do it any faster than that, you'll just end up being frustrated, and make no progress.
 
Agreed. But I just want to learn some basic concepts in this area, as this is not the main objective (I mean, it's only a "local" objective). I've already found some books and articles that are being really helpful (Ott E. Chaos in Dynamical Systems, for example, has a great discussion in it's final chapters)
 

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