Related papers: Why are inner planets not inclined?
We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with…
Proto-planetary discs, the birth environment of planets, are an example of a structure commonly found in astrophysics, accretion discs. Identifying the mechanism responsible for accretion is a long-standing problem, dating back several…
The apparent regularity of the motion of the giant planets of our solar system suggested for decades that said planets formed onto orbits similar to the current ones and that nothing dramatic ever happened during their lifetime. The…
Stably-stratified layers may be present at the top of the electrically-conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the…
Many astrophysical phenomena (such as the slow rotation of neutron stars or the rigid rotation of the solar core) can be explained by the action of the Tayler instability of toroidal magnetic fields in the radiative zones of stars. In order…
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with the velocity vector making a small positive angle with the boundary. Lazutkin proved that in two dimensions, it is impossible for this angle…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems…
We test the effect of assumptions about stellar motion on the behavior of gravitational instabilities in protoplanetary disks around solar-type stars by performing two simulations that are identical in all respects except the treatment of…
We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…
The known extrasolar multiple-planet systems share a surprising dynamical attribute: they cluster just beyond the Hill stability boundary. Here we show that the planet-planet scattering model, which naturally explains the observed exoplanet…
The text of lectures to the 2011 Tenerife Winter School. The School's theme was "Secular Evolution of Galaxies" and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and…
In the 1960s, it has been substantiated that an equation of Schrodinger type could describe the diffusion phenomena, and the main consequence from this finding has been that there would be wave property in the diffusion processes as well.…
The temperature in most parts of a protoplanetary disk is determined by irradiation from the central star. Numerical experiments of Watanabe \& Lin (2008) suggested that such disks, also called `passive disks', suffer from a thermal…
In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the…
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary…
The anomalously large radii of strongly irradiated exoplanets have remained a major puzzle in astronomy. Based on a 2D steady state atmospheric circulation model, the validity of which is assessed by comparison to 3D calculations, we reveal…
The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a time-periodic perturbation…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…