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Wimberger S., Nonlinear Dynamics and Quantum Chaos, Springer Graduate Texts in Physics (2014).
Arnol'd, V. I., Mathematical methods of classical mechanics, Springer-Verlag 2nd edition (1989).
- Ozorio de Almeida, A. M., Hamiltonian systems : Chaos and quantization, Cambridge University Press (1988).
- Strogatz, S.H.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering, Westview Press Classroom Classics (2014).
- Scheck, F.: Mechanics: From Newton's Laws to Deterministic Chaos , Springer-Verlag Berlin Heidelberg, (2010).
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Course contents
Lecture 01: Examples of elementary dynamical systems | Lecture 09: Lagrangean variational principles (14.03) |
| Lecture 02: Existence and uniqueness theorems for ODE’s (01.02) | Lecture 10: Hamiltonian variational principle |
| Lecture 03: Hamiltonian vector fields and time reversal (08.02) | Lecture 11: Noether's first and second theorem |
| Lecture 04: Linear systems, Hartman-Grobman theorem (08.02) | Lecture 12: Equivariance and Poisson brackets |
| Lecture 05: Linear autonomous Hamiltonian systems (11.02) | Lecture 13: Canonical transformations |
| Lecture 06: Linear periodic systems and stability of periodic orbits | Lecture 14: Hamilton--Jacobi and dynamic programming |
| Lecture 07: Poincaré section, periodic orbits and Poincaré recurrence (02.03) | Lecture 15: Liouville Arnold integrable systems |
| Lecture 08: D'Alembert principle and Euler–Lagrange equations (04.03) | Lecture 16: Birkhoff integrable systems |
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