seminar: Normal form theorems in Elliptic and Parabolic dynamic
speaker: Nukos Karalaliolios (Imperial College London)abstract: We will discuss some normal form theorems for perturbations of the main examples of elliptic and parabolic dynamics, generalizing the classical theorem due to Arnol'd and Moser, on perturbations of Diophantine translations in tori. Such theorems try to establish that the orbit of a certain type of diffeomorphism under the relevant notion of conjugation is locally a closed submanifold of a certain codimension. Subsequently, one tries to interpret the perturbations in transversal directions as perturbations that modify the dynamics of the studied diffeomorphism.
We will discuss normal form theorems in the following settings: 1. that of commuting diffeomorphisms of the torus, close to Simultaneously Diophantine rotations. This provides a new, more general and stronger proof of a theorem by Moser on the simultaneous linearizability of such dynamical systems. 2. that of periodic translations in tori. 3. the case of Resonant Diophantine translations, which is intermediate between the periodic case and the classical normal form theorem. 4. the parabolic mapping (skew-shift) of the torus T2.
timetable:
Wed 4 Apr, 14:45 - 15:45, Sala Conferenze Centro De Giorgi
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