相关论文: Potential wells with a unique brake orbit. Counter…

In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…

In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\in C^2(\Bbb R^{2n}, \Bbb R)$ is super-quadratic and convex, for every number…

Under weaker regularity and compactness assumptions, we find the mountain-pass essential point, which is a novel extension of the classical Ambrosetti-Rabinowitz mountain pass theorem. We study the reversible superquadratic autonomous…

In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key…

This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere,…

In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds. Hofer-Zehnder conjecture states that a Hamiltonian diffeomorphisms has infinitely many periodic…

We consider Hamiltonian functions of classical type, namely even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton's equations such that the generalized momenta are zero on two different…

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…

For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti…

Let $H: \mathbb{R}^4 \to \mathbb{R}$ be any smooth function. This article introduces some arguments for extracting dynamical information about the Hamiltonian flow of $H$ from high-dimensional families of closed holomorphic curves. We work…

The existence of parabolic orbits is obtained for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of non-collision periodic solutions which are obtained by Mountain Pass Lemma.

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the…

Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space $E_2$ are explored. The study is restricted to Hamiltonians allowing separation of variables $V(x,y)=V_1(x)+V_2(y)$ in Cartesian coordinates. In particular,…

We consider a class of two-degree-of-freedom Hamiltonian systems with saddle-centers connected by heteroclinic orbits and discuss some relationships between the existence of transverse heteroclinic orbits and nonintegrability. By the…

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to…

Motivated by our earlier argument that the apparent large cosmological constant from quantum fluctuations is actually an artifact of not using a full quantum mechanical superposition to determine the ground state in which the universe lives…

The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…

We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has infinitely many simple periodic points. This provides a vast…

We consider a natural Hamiltonian system with two degrees of freedom and Hamiltonian $H=\|p\|^2/2+V(q)$. The configuration space $M$ is a closed surface (for noncompact $M$ certain conditions at infinity are required). It is well known that…