SIMBa: Probabilistic methods in small divisors problems

03/02/2014 by blocmat Deixa un comentari

Dilluns, 3 de febrer, se celebrarà una nova sessió del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Piotr Kamienski
Universitat: Instytut Informatyki (Uniwersytetu Jagiellonskiego)

Data: Dilluns, 20 de gener de 2014
Hora: 17:45, cafè i galetes; 18:00, inici
Lloc: Aula IMUB (al terrat), Facultat de Matemàtiques de la Universitat de Barcelona.

Títol: Probabilistic methods in small divisors problems
Resum: In my talk I will consider one of the least complicated small divisors questions – when is a small perturbation of a constant vector field $(1, \omega)$ on the 2-torus equivalent to this vector field? KAM theory tells us that this happens under a diophantine condition on $\omega$ and that the admissible size of perturbation is closely related to the diophantine “quality” of this number. I will show that with probability close to 1 you don’t need all the arithmetical information about $\omega$ . Namely for any $p>0$ there is an (explicitly given) integer $N(p)$ such that for a randomly chosen $\omega$ with probability $1-p$ the admissible perturbation size in this KAM theorem depends only on the first $N(p)$ digits of $\omega$ . The proof uses, apart from standard KAM techniques, the properties of the Khintchine constant.

Si voleu rebre informació dels propers seminaris us podeu subscriure a la llista de correu. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.