Related papers: Generic Nekhoroshev theory without small divisors

We prove the existence of infinitely many time-periodic solutions of nonlinear Schr\"odinger equations using pseudo-holomorphic curve methods from Hamiltonian Floer theory. For the generalization of the Gromov-Floer compactness theorem to…

We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…

The Krylov-Safonov theorem says that solutions to non-divergence uniformly elliptic equations with rough coefficients are H\"{o}lder continuous. The proof combines a basic measure estimate with delicate localization and covering arguments.…

In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity…

We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes slightly improving the stable range given by the traditional…

The inhomogeneous Khintchine-Groshev Theorem is a classical generalization of Khintchine's Theorem in Diophantine approximation, by approximating points in $\mathbb{R}^m$ by systems of linear forms in $n$ variables. Analogous to the…

We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The…

We consider a mechanical system consisting of $n$ penduli and a $d$-dimensional generalized rotator subject to a time-dependent perturbation. The perturbation is not assumed to be either Hamiltonian, or periodic or quasi-periodic. The…

We prove that in the Ryabov paper an application of the geometric Kharlamov method to the Goryachev system yields noncommutative "new variables of separation" instead of the standard canonical variables of separation.

This paper develops the hybridizable discontinuous Galerkin (HDG) method for the Ostrovsky equation, a nonlinear dispersive wave equation featuring both third-order dispersion and a nonlocal antiderivative term with Coriolis effect. On a…

We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…

We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we can get the bounds for the perturbation, the variation of…

We improve the global Nekhoroshev stability for analytic quasi-convex nearly integrable Hamiltonian systems. The new stability result is optimal, as it matches the fastest speed of Arnold diffusion.

In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on…

In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…

In this paper we present new stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions. To obtain error estimates without elliptic regularity assumptions, we…

We consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits…

For stochastic perturbations of linear systems with non-zero pure imaginary spectrum we discuss the averaging theorems in terms of the slow-fast action-angle variables and in the sense of Krylov-Bogoliubov. Then we show that if the…

A nonsymmetric gravitational theory (NGT) is presented which is free of ghost poles, tachyons and higher-order poles and there are no problems with asymptotic boundary conditions. An extended Birkhoff theorem is shown to hold for the…

We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) $O(\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with…