Geometric Structures seminar - Alessandro Portaluri - March 24, 2022

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker:   Alessandro Portaluri<https://sites.google.com/view/alessandro-portaluri/> (University of Torino)

Title:         Spectral stability, spectral flow and circular relative equilibria for the  Newtonian n-body problem

Time:        March 24, 2022, 2:00 pm (Rome Time)



Venue - hybrid:

  *   at room 134 at SISSA
  *
  *   from remote, on zoom at this link

https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria (RE), namely solutions in which each body rigidly rotates about the center of mass and the configuration of the whole system is constant in time and central configuration. A classical problem in celestial mechanics aims at relating the (in-)stability properties of a (RE) to the index properties of the central configuration generating it.
In this talk, we discuss some  sufficient conditions that imply the spectral instability of planar and non-planar (RE)  generated by a central configuration.
The key ingredients are a new formula  that allows to compute the spectral flow of a path of symmetric matrices having degenerate starting point, and a symplectic decomposition of the phase space of the linearized Hamiltonian system along a given (RE)  which allows us to rule out the uninteresting part of the dynamics corresponding to the translational and (partially) to the rotational symmetry of the problem.
This talk is based on a recent joint work with Prof. Dr. Luca Asselle (Ruhr Universit\"at  Bochum, Germany)   and Prof. Dr. Li Wu (Shandong University, Jinan, China).

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More information and the abstract of the talk as a pdf file can be found here: https://sites.google.com/view/geometric-structures/

Everyone is welcome!


--
Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/