Minicourse of An introduction to the geometry of integrable Hamiltonian systems

Minicourse of An introduction to the geometry of integrable Hamiltonian systems

Dear students of the Master degree in Mathematics,

 

the minicourse in

 

An introduction to the geometry of integrable Hamiltonian systems

 

speaker prof. Daniele Sepe - UFF Niteroi, Brazil, start next Tuesday October 20th.

 

Schedule:

 

- Tuesday 20/10/2020, 14:00-16:00,

 

- Thursday 22/10/2020, 16:00-18:00,

 

- Thursday 29/10/2020, 15:00-17:00,

 

- Friday  30/10/2020, 15:00-17:00.

 

The lessons of the minicourse will be broadcasted streaming via Zoom, recorded and then available. People interested are invited to register to the moodle of the  minicourses,

 

https://www.di.univr.it/?ent=oi&codiceCs=S72&codins=4S009660&cs=389&discr=&discrCd=

 

where all the information, materials and zoom links will be available.

To facilitate fast communications and to allow people that has not the univr credentials to attend the minicourse, a telegram group has been created. Please register also there https://t.me/minicourseGHS.

 

For any information don’t hesitate to contact me (dott. Nicola Sansonetto) organiser of the minicourse.


Nicola Sansonetto

 

 

Abstract.

An important question in Hamiltonian mechanics is to describe qualitative properties of the dynamics under consideration. In general, this is a hard problem but it can be tackled for those systems that are known to be integrable, i.e. that admit the largest number of constants of motion. In spite of their relatively simple dynamical behaviour, integrable Hamiltonian systems play a prominent role in Hamiltonian mechanics and beyond, ranging from symplectic geometry, Lie theory and quantum mechanics. The aim of this course is to provide an introduction to the geometry of such systems from a symplectic perspective. After introducing the necessary tools from symplectic geometry, we will study the structure of integrable Hamiltonian systems near regular points and regular (connected components of) fibres, proving the Darboux-Carathéodory and the Liouville-Arnol'd theorems. The theory will be illustrated by some (simple) examples.

Publication date
Wednesday, October 14, 2020 - 10:34:23 AM
Subject
Minicourse of An introduction to the geometry of integrable Hamiltonian systems
Published by
Nicola Sansonetto
Analytical mechanics (2020/2021)
Numerical modelling and optimization - MODELLING SEMINAR (2020/2021)
Bachelor's degree in Applied Mathematics
Master's degree in Mathematics