**David Merritt**and the mathematician

**June Barrow-Green**will be at Milano for two distinct talks.

Merritt will be at the Osservatorio Astronomico di Brera for the following talk:

**Relativistic Dynamics at the Centers of Galaxies**(h 14:00)

Encounters between stars and stellar remnants at the centers of galaxies drive many important processes, including generation of gravitational waves via extreme-mass-ratio inspirals (EMRIs). The fact that these encounters take place near a supermassive black hole (SMBH) turns out to be important for two reasons: (1) The orbital motion is quasi-Keplerian, so that correlations are maintained for much longer than in purely random encounters. (2) Relativity affects the motion, through mechanisms like precession of the periapse and frame-dragging. The interplay between these processes is just now beginning to be understood, based on N-body simulations that contain a post-Newtonian representation of relativistic dynamics. A key result is that relativity can be important even for orbits that extend outward to a substantial fraction of the SMBH influence radius, by destroying the long-term correlations that would otherwise drive the evolution. I will discuss this work and its implications for the EMRI problem, for experimental tests of theories of gravity, and for the long-term evolution of SMBHs and galactic nuclei.And June Barrow-Green will be at Mathematics Department "Federigo Enriques" with the talk^{(1)}

*PoincarÃ© and the three body problem*.

^{(2)}(h 16:30)

The problem was stated by PoincarÃ© in 1890 with the following quotation:

I consider three masses, the first very large, the second small but finite, the third infinitely small; I assume that the first two each describe a circle around their common centre of gravity and that the third moves in the plane of these circles. An example would be the case of a small planet perturbed by Jupiter, if the eccentricity of Jupiter and the inclination of the orbits are disregarded.^{(3)}

(1) From inSPIRE I found the following paper,

*Towards relativistic orbit fitting of Galactic center stars and pulsars*(arXiv), that seems about the subject of the thalk.

(2) From the introduction of

*Oscar II's prize competition and the error in PoincarÃ©'s memoir on the three body problem*by June Barrow-Green:

In the autumn of 1890 Henri PoincarÃ©'s memoir on the three body problem was published in the journal Acta Mathematica as the winning entry in the international prize competition sponsored by Oscar II, King of Sweden and Norway, to mark his 60th birthday on January 21, 1889. Today, PoincarÃ©'s published memoir is renowned for containing the first mathematical description of chaotic behavior in a dynamical system. Correspondence preserved at the Institut Mittag-Leffler reveals that the competition was beleaguered by difficulties throughout. In particular, it has emerged that only weeks before the prize-winning memoir was due to be published, PoincarÃ© discovered an error in his work which forced him to make very substantial changes. Indeed it was only as a result of correcting the error that he discovered the existence of what today are known as homoclinic points. This paper is an account of the troubled history of the competition together with an explanation of the error in PoincarÃ©'s memoir.(3) Quotation extracted from

*PoincarÃ© and the Three Body Problem*

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