相关论文: Minimal period estimates for brake orbits of nonli…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…

Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of…

For any $n\ge 2$, $\Omega\subset\rn$, and any given convex and coercive Hamiltonian function $H\in C^{0}(\rn)$, we find an optimal sufficient condition on $H$, that is, for any $c\in\mathbb R$, the level set $H^{-1}(c)$ does not contains…

We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph $G=\gc$. In this model $G$ is drawn uniformly from graphs with vertex set $[n]$, $m$ edges and minimum degree at least three. We focus on…

M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid…

We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three.

In this paper, by the Masolv index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions

This paper presents sufficient conditions for Hamiltonian paths and cycles in graphs. Letting $\lambda\left( G\right) $ denote the spectral radius of the adjacency matrix of a graph $G,$ the main results of the paper are: (1) Let $k\geq1,$…

In this paper we consider the existence of Hamilton cycles in the random graph $G=G_{n,m}^{\delta\geq 3}$. This a random graph chosen uniformly from the set of graphs with vertex set $[n]$, $m$ edges and minimum degree at least 3. Our…

Higher precision efficient computation of period 1 relaxation oscillations of strongly nonlinear and singularly perturbed Rayleigh equations with external periodic forcing is presented. The computations are performed in the context of…

Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries…

The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy $\epsilon_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an…

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…

A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…

We present an algorithm CRE, which either finds a Hamilton cycle in a graph $G$ or determines that there is no such cycle in the graph. The algorithm's expected running time over input distribution $G\sim G(n,p)$ is $(1+o(1))n/p$, the…

The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…

The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are…

Let $P$ be a connected bounded region in the plane formed out of $2 \times 2$ blocks joined by their sides. Peng and Rascoussier conjectured that all minimum-turn Hamiltonian cycles of $P$ exhibit a certain regular structure. We prove this…

For many classes of symplectic manifolds, the Hamiltonian flow of a function with sufficiently large variation must have a fast periodic orbit. This principle is the base of the notion of Hofer-Zehnder capacity and some other symplectic…

We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits,…