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Contact Geometry in Dynamics: the 3-Body Problem

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We have known for a long time how to write down the equations of motion of a satellite that moves under the influence of the gravitational fields of the Earth and the Moon, but surprisingly, we still do not fully understand the long term behaviour of the satellite since we cannot explicitly solve the equations. At the end of the 19th century, Poincare noticed the presence of chaos in the system and kick-started the modern theory of dynamical systems. Recently a new type of geometry called contact geometry (the odd dimensional relative of symplectic geometry) has been proposed as a tool for understanding this old problem in celestial mechanics. In the talk I will try to explain what contact geometry is and why it is relevant for the 3-body problem.

This talk is part of the Trinity Mathematical Society series.

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