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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Integrability and beyond

The course is not on the list Without time-table
Code Completion Credits Range Language
D02INB ZK English
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Physics
Synopsis:

Hamiltonian systems and their integrals of motion. Hamilton-Jacobi equation and separation of variables. Classification of integrable systems with integrals polynomial in momenta. Superintegrability. Perturbative methods in the study of Hamiltonian systems.

Requirements:
Syllabus of lectures:

1. Review of Hamiltonian mechanics - Poisson brackets, equations of motion, integrals of motion, Hamilton-Jacobi equation

2. Separation of variables in Hamilton-Jacobi equation, action-angle variables

3. Levi-Civita condition for separability, separation in orthogonal coordinate systems, relation of separability to the existence of integrals of motion

4. Conditions determining integrals of motion polynomial in the momenta in the Euclidean space

5. Classification of 2D & 3D quadratically integrable systems

6. Superintegrability, polynomial algebras of integrals

7. Stackel transformation, relation between the isotropic harmonic oscillator and Coulomb problem

8. Perturbations of integrable and superintegrable systems

9. Normalization and bifurcations around resonances

Syllabus of tutorials:
Study Objective:
Study materials:

Key references:

[1] M. Audin: Hamiltonian Systems and Their Integrability. American Mathematical Society, 2008

[2] W. Miller Jr., S. Post and P. Winternitz: Classical and quantum superintegrability with applications, J. Phys. A: Math. Theor. 46 423001, 2013

Recommended references:

[3] E. G. Kalnins, J. M. Kress and W. Miller Jr.: Separation of variables and superintegrability : the symmetry of solvable systems, Institute of Physics Publishing, 2018

[4] J. A. Sanders, F. Verhulst, J. Murdock: Averaging Methods in Nonlinear Dynamical Systems, Springer 2007

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-03-29
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