Related papers: Monotone flows with dense periodic orbits

We prove that for a certain class of closed monotone symplectic manifolds any Hamiltonian diffeomorphism with a hyperbolic fixed point must necessarily have infinitely many periodic orbits. Among the manifolds in this class are complex…

A general type of mathematical argument is described, which applies to all the cases in which dynamo maintenance of a steady magnetic field by motion in a uniform density is known to be impossible. Previous work has demonstrated that…

Assume that a Hamiltonian system is monotone. In this paper, we give several characterizations on when such a system is Anosov. Assuming that a monotone Hamiltonian system has no conjugate point, we show that there are two distributions…

In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product…

Let M be a weakly monotone symplectic manifold, and H be a time-dependent Hamiltonian; we assume that the periodic orbits of the corresponding time-dependent Hamiltonian vector field are non-degenerate. We construct a refined version of the…

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…

In this paper we present a characterization of the symmetric rotational periodic gravity water waves of finite depth and without stagnation points in terms of the underlying flow. Namely, we show that such a wave is symmetric and has a…

We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S^1 spaces. Additionally, we show that all these spaces are Kaehler, that every such space is obtained from a…

In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…

A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is…

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…

We prove that for every three-dimensional vector field, either it can be accumulated by Morse-Smale ones, or it can be accumulated by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit in the $C^1$ topology.

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional

We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector…

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…

Let $\Gamma\subset PSL(2,\mathbb{R})$ be such that the space $X=\Gamma\backslash PSL(2,\mathbb{R})$ is not compact. Let $(h_t)$ be the horocycle flow acting on $X$. We show that for every $x\in X$ that is not periodic for $(h_t)$ and for…

In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\geq 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order…

In this sequel paper we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a…

In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…