M. Davies (Lund University, Department of Astronomy and Theoretical Physics, Lund, Sweden),
F. Adams (University of Michigan, United States),
P. Armitage (University of Colorado, Boulder, JILA, United States),
J. Chambers (Carnegie Institution of Washington, DTM, United States),
E. Ford (University of Florida, Department of Astronomy, United States),
A. Morbidelli (Observatoire de la Cote d'Azur, Nice, France),
S. Raymond (University of Bordeaux, Department of Astronomy, France),
D. Veras (University of Cambridge, Institute of Astronomy, United Kingdom)

This talk/chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions at play in our own Solar System. We then describe how these change when one considers more tightly-packed planetary systems with some systems becoming dynamically unstable as planet-planet interactions grow leading to strong encounters and ultimately either ejections or collisions of planets. We first discuss the basic physical processes at play and then consider how these processes apply to extrasolar planetary systems and what constraints are provided by observed systems. The presence of a residual planetesimal disc can lead to planetary migration and may cause instabilities induced by resonance crossing, although such discs may also stabilise a planetary system. The crowded birth environment of a planetary system can have a significant impact: close encounters and binary companions may act to destabilise a system. In particular, in the latter case the Kozai mechanism may place planets on extremely eccentric orbits which may later circularise to produce hot jupiters.

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