Seminario: Nonintegrability of the Zipoy-Vorhees metric

Mercoledì 19 Febbraio 2014, ore 16:00 - Aula 1BC45 - Vladimir Matveev



Mercoledì 19 Febbraio 2014 alle ore 16:00 in aula 1BC45, Vladimir Matveev terrà un seminario dal titolo "Nonintegrability of the Zipoy-Vorhees metric"

I will consider natural Hamiltonian systems with two degrees of freedom and speak about the existence and nonexistence of integrals that are polynomial in momenta. This is a classical topic: I will start with a historical overview and explain the classical and modern motivation. In the mathematical part of my talk, I will mostly discuss the following questions: given a metric, how to prove the (non)existence of an integral of a given degree, and how to find it explicitly? I will explain the classical and modern methods to study this question. As an application, I will present new systems admitting an integral of degree 3 in momenta and a solution of a problem explicitly stated by J. Brink (partially joint with H. Dullin, V. Shevchishin, B. Kruglikov).
The talk will be understandable for mathematicians from other fields and will emphasize how the algebraic geometry methods could be used in mathematical physics and differential geometry.