Related papers: KAM \`{a} la R
In this paper, we study infinite-dimensional Lagrangian systems where the potential functions are periodic, rearrangement invariant and weakly upper semicontinuous. And we prove that there exists a calibrated curve for every $M\in…
Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed…
The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori…
We present a rigorous dynamical systems analysis of tubular origami tessellations by identifying the inverse module number, $N^{-1}$, as a perturbation parameter within the framework of Kolmogorov-Arnold-Moser (KAM) theory. In the…
We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…
In this paper, we present an algorithm to computea fiberwise Lagrangian torus in quasi-periodic (QP) Hamiltonian systems, whose convergence is proved in the [CHP25]. We exhibit the algorithm with two models. The first is a Tokamak model…
The KAM (Kolmogorov-Arnold-Moser) theorem guarantees the stability of quasi-periodic invariant tori by perturbation in some Hamiltonian systems. Michel Herman proved a similar result for quasi-periodic motions, with $k$-dimensional…
We investigate the dynamics of the quasi-periodic swing equations from the perspective of weak KAM theory. To this end, we firstly study a class of Hamiltonian systems. We obtain that the limit $u$, which derived from convergence of a…
We develop an a-posteriori KAM theory for the equilibrium equations for quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the frequency of the solutions resonates with the frequencies of the substratum. The KAM…
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
In this work, we obtain an a-posteriori theorem for the existence of partly hyperbolic invariant tori in analytic Hamiltonian systems: autonomous, periodic, and quasi-periodic. The method of proof is based on the convergence of a KAM…
In this paper, we study the Hamiltonian systems $ H\left( {y,x,\xi ,\varepsilon } \right) = \left\langle {\omega \left( \xi \right),y} \right\rangle + \varepsilon P\left( {y,x,\xi ,\varepsilon } \right) $, where $ \omega $ and $ P $ are…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis…
In this paper, we prove the existence of full dimensional invariant tori for a non-autonomous, almost-periodically forced nonlinear beam equation with a periodic boundary condition via KAM theory.
Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure…
In this short note, I explain how the non-degeneracy condition of the KAM can be bypassed. The first version of the note has been submitted for publication back in 2010 and this version in 2012.
We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the…
Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low…