Related papers: Normal forms for the Laplace resonance
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…
We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1:2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations.…
Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active…
For each simple euclidean Jordan algebra $V$ of rank $\rho$ and degree $\delta$, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler problem for planetary…
Quantum phase transitions in the two-dimensional Kugel-Khomski model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization ansatz. When $3z^2-r^2$ orbitals are favored by the crystal…
We consider a $(7 + k)$-dimensional Einstein-Gauss-Bonnet model with the cosmological $\Lambda$-term. A cosmological model with three factor spaces of dimensions $3$, $3$ and $k$, $k > 2$ is considered. Exact stable solutions with three…
The Kepler mission has discovered a plethora of multiple transiting planet candidate exosystems, many of which feature putative pairs of planets near mean motion resonance commensurabilities. Identifying potentially resonant systems could…
We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parametrisation of the phase space…
We present a framework for non-singular bouncing cosmology in a closed ($k=+1$) universe with a two-field sigma model whose regularized hyperbolic field-space metric $g^S_{\chi\chi}(\phi) = (1 + e^{-2\alpha\phi/M_{\mathrm{Pl}}})^{-1}$ is…
On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar charged fermions interacting by means of classical and phantom…
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
The purpose of this article is to compute the normal form of a class of general quadratic Hamiltonian systems that generalizes naturally Euler's equations from the free rigid body dynamics.
We investigate the correspondence between classical noise and quantum environments. Although it has been known that the classical noise can be mapped to the quantum environments only for pure dephasing and infinite-temperature dissipation…
Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On…
We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation…
A normal form theory for non--quasi--periodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in [15] to prove, in the averaged, planar three--body problem, the existence of a plenty…
In earlier work, Lomeli and Meiss used a generalization of the symplectic approach to study volume preserving generating differential forms. In particular, for the $\mathbb{R}^3$ case, the first to differ from the symplectic case, they…
A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the…
We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly describe the reduced phase space for this Hamiltonian…
Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of $p$-Laplacian type, with square-integrable right-hand sides and initial data…