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# Introduction to Hamiltonian Dynamics, Spring 2017

Teacher: Paolo Muratore-Ginanneschi

Scope: 7 cr

Teaching:

Topics: Classical Mechanics, Lagrange and Hamiltonian formalism, Chaos in Nonlinear Hamiltonian Dynamics.

Prerequisites:

## Teaching schedule

16.1.-14.5.2017, Tue from 10-12, room C122. Exercise group Thu 10-12, room C122.

## Exams

Exam lasts 2,5 hours.

You can use (lecturer will fill in) in the exam.

## Course material

The course will draw mostly from the following references.

## 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

Lecture notes available from the latest installment of this course.

## Registration

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## Exercises

### Assignments

• Exercise set 1 (09.02)
• Exercise set 2 (14.02)
• Exercise set 3 (27.02)
• Exercise set 4 (01.03)
• Exercise set 5 (14.03)
• Exercise set 6 (29.03: one typo corrected in assignment 1)
• Exercise set 7
• Exercise set 8
• Exercise set 9

### Exercise classes

GroupDayTimeRoomInstructor
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## Course feedback

Course feedback can be given at any point during the course. Click here.

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