Dia: Dimecres 12 de novembre de 2025
Lloc: Aula S03, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Guowei Yu, Nankai University
Títol: (Bi)-hyperbolic and (bi)-parabolic motions in the restricted (N+1)-body problem
Resum: According to Chazy, the final motion of the restricted (N+1)-body problem has four possibilities: bounded, hyperbolic, parabolic and oscillatory. When the motion is hyperbolic or parabolic, the massless body will go to infinity along a definite asymptotic direction with a finite limiting energy. Then there are two basic questions: First given any initial time and position, as well as the asymptotic direction and limiting energy when time goes to positive infinity, is there a corresponding hyperbolic or parabolic motion realizing it; Second given any asymptotic directions and limiting energy, when time goes to both negative and positive infinity, it there a corresponding bi-hyperbolic or bi-parabolic motion realizing it? In this talk, we will report some of our progress in these two questions.
A càrrec de: Sergi Burniol Clotet, Universidad de la República, Uruguai
Títol: Rigidity of the Unstable Foliation
Resum: Anosov flows are one of the central examples of hyperbolic and chaotic dynamical systems. Associated to them are the stable and unstable foliations, whose leaves contract and expand exponentially along the flow. In this talk, we present a rigidity result for these foliations in the case of transitive Anosov flows on 3-manifolds: if the unstable foliations of two such flows are equivalent (that is, if there exists a homeomorphism mapping one foliation to the other), then the flows are topologically conjugate up to a constant change of time.
The classical examples of Anosov flows are the geodesic flows of compact negatively curved surfaces. In this setting, there are previous rigidity results due to Ratner, Marcus, and Abe, among others. The latter showed that if the unstable foliations of two such flows are equivalent, then the underlying surfaces are homothetic.
Last updated: Wed Nov 12 18:01:16 2025