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As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula. [ABSTRACT FROM AUTHOR]

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula. [ABSTRACT FROM AUTHOR]

Massive planets form within the lifetime of protoplanetary disks, and therefore, they are subject to orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk, its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first-order resonances, but the method can be easily generalized. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter nevertheless play the decisive role in the destabilization of resonant pairs. We show evidence that as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable. [ABSTRACT FROM AUTHOR]