相关论文: Invariant curves of almost periodic twist mappings
In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all…
In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear…
In this paper we are concerned with the existence of invariant curves of planar mappings which are quasi-periodic in the spatial variable, satisfy the intersection property, $\mathcal{C}^{p}$ smooth with $p>2n+1$, $n$ is the number of…
The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the…
We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…
Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total…
In this paper we study the dynamical behaviour of the differential equation \begin{equation*} x''+ax^+ -bx^-=f(t), \end{equation*} where $x^+=\max\{x,0\}$,\ $x^-=\max\{-x,0\}$, $a$ and $b$ are two different positive constants, $f(t)$ is a…
A method via the KAM technique is introduced to study the existence of invariant tori and quasiperiodic solutions for impulsive Duffing-type equations with time period 1. Basing on several planar symplectic homeomorphisms and some estimates…
In this paper we are concerned with the existence of periodic solutions for semilinear Duffing equations with impulsive effects. Firstly for the autonomous one, basing on Poincar\'{e}-Birkhoff twist theorem, we prove the existence of…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
In this paper, we obtain the invariant curves of quasi-periodic reversible mappings with finite smoothness. Since the reversible property is difficult to maintain in the process of approximating smooth functions by analytical ones,…
In this note, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and…
This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel…