Related papers: Normal form for lower dimensional elliptic tori in…
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous…
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems…
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with…
We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; ``in general'' means for a generic class of holomorphic…
In this paper, we present evidence of the stability of a simplified model of the Solar System, a flat (Newtonian) Sun-Jupiter-Saturn system with realistic data: masses of the Sun and the planets, their semi-axes, eccentricities and…
In this paper by reduction we construct a family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$ as the image of the composition of the Hopf map $\mathcal{H}: \mathbb{S}^7\to \mathbb{CP}^3$ and a map…
We construct a family of flat isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$ and find necessary and sufficient conditions for their Hamiltonian minimality.
A major achievement of Dewar and coworkers is the SPEC code to construct stepped-pressure equilibria in magnetohydrostatics without axisymmetry. Their existence had been proved by Bruno and Laurence. As part of the procedure of Bruno and…
The goal of this paper is to provide a methodology to prove existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same…
A fundamental premise of Hamiltonian chaos is the existence and properties of tori in phase space. More than a geometrical construct, these structures underlie the very dynamics of both classical and quantal systems. Although presented in…
This paper demonstrates sufficient conditions for the existence of KAM tori in a singly thermostated, integrable hamiltonian system with $n$ degrees of freedom with a focus on the generalized, variable-mass thermostats of order 2--which…
We study the existence of whiskered tori in a family $f_\mu$ of conformally symplectic maps depending on parameters $\mu$. Whiskered tori are tori on which the motion is a rotation, but they have as many expanding/contracting directions as…
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…
A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…
The Hamiltonian shape invariant of a domain $X \subset \mathbb R^4$, as a subset of $\mathbb R^2$, describes the product Lagrangian tori which may be embedded in $X$. We provide necessary and sufficient conditions to determine whether or…
In the previous paper, the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori.…
We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually…
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the…
The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia of Mathematical Sciences \cite{AKN1}, and in subsequent…