arXiv subjects

J. Laskar

Publications and source records attributed to J. Laskar.

130 records · Page 8Linked to original sources

arXiv2005

A pair of planets around HD 202206 or a circumbinary planet?

Long-term precise Doppler measurements with the CORALIE spectrograph reveal the presence of a second planet orbiting the solar-type star HD202206. The radial-velocity combined fit yields companion masses of m_2\sini = 17.4 M_Jup and 2.44 M_Jup, semi-major axes of a = 0.83 AU and 2.55 AU, and eccentricities of e = 0.43 and 0.27, respectively. A dynamical analysis of the system further shows a 5/1 mean motion resonance between the two planets. This system is of particular interest since the inner planet is within the brown-dwarf limits while the outer one is much less massive. Therefore, either the inner planet formed simultaneously in the protoplanetary disk as a superplanet, or the outer Jupiter-like planet formed in a circumbinary disk. We believe this singular planetary system will provide important constraints on planetary formation and migration scenarios.

astro-ph↗

arXiv2001

Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverge is the same as the value given by the frequency map analysis for the break-up of invariant tori. Furthermore, we obtain by these methods numerical values of the threshold of the break-up of the last invariant torus.

nlin.CD↗

arXiv2000

High order symplectic integrators for perturbed Hamiltonian systems

We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+εB$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps with a remainder of order $O(τ^pε+τ^2ε^2)$, where $τ$ is the stepsize of the integrator. The analytical expressions of the leading terms of the remainders are given at all orders. In many cases, a corrector step can be performed such that the remainder becomes $O(τ^pε+τ^4ε^2)$. The performances of these integrators are compared for the simple pendulum and the planetary 3-Body problem of Sun-Jupiter-Saturn.

astro-ph↗

arXiv2000

Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis

We study the behaviour of the Standard map critical function in a neighbourhood of a fixed resonance, that is the scaling law at the fixed resonance. We prove that for the fundamental resonance the scaling law is linear. We show numerical evidence that for the other resonances $p/q$, $q \geq 2$, $p \neq 0$ and $p$ and $q$ relatively prime, the scaling law follows a power--law with exponent $1/q$.

nlin.CD↗