Programma: PRIN
Responsabile scientifico per il dipartimento: Marco Lenci
Struttura principale: DIFA
Data inizio e data fine: dal 28/09/2023 al 28/09/2025
Sistemi dinamici: nuove frontiere della matematica
Il progetto affronta problemi aperti nei sistemi dinamici, come leggi limite, sistemi iperbolici e con molti gradi di libertà, con modelli generali e specifici per avanzare lo stato dell’arte.
Dynamical Systems: New Frontiers in Mathematics
The project tackles open problems in dynamical systems—limit laws, hyperbolic and high-dimensional systems—using general and specific models to advance the state of the art.
Abstract
Some outstanding open problems in the field of Dynamical systems are: the derivation of precise limit lawsfor smooth hyperbolic systems, the study of partially hyperbolic systems, discontinuous systems, extendedsystems, systems with many, possibly infinitely many, degrees of freedom, and systems with mixed phasespace. Our objective is to address the above-mentioned momentous problems by investigating general systems andspecific models that we believe will shed light on general issues. While our final goals are highly ambitious,and hence very risky, all the intermediate achievements of our project are of great interest in themselves.Therefore, any partial success in this research program would constitute a significant advance of the state ofthe art. In addition, as we detail shortly, many tasks are interconnected, so any advance in one will facilitateadvances in the others.