相关论文: On the topological entropy of an optical Hamiltoni…
We prove that every $C^1$ three-dimensional flow with positive topological entropy can be $C^1$ approximated by flows with homoclinic orbits. This extends a previous result for $C^1$ surface diffeomorphisms \cite{g}.
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
In this article we study persistence features of topological entropy and periodic orbit growth of Hamiltonian diffeomorphisms on surfaces with respect to Hofer's metric. We exhibit stability of these dynamical quantities in a rather strong…
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced…
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a…
Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec} E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly…
The main result in this paper is the $C^{\infty}$ closing lemma for a large family of Hamiltonian flows on $4$-dimensional symplectic manifolds, which includes classical Hamiltonian systems. First we prove the $C^{\infty}$ closing lemma and…
We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\mathtt{a}\mapsto \mathtt{baa}$ and $\mathtt{b} \mapsto \mathtt{ab}$ with probability $p$ and…
We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…
Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the…
We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
The Lagrangian description of fluid flow in relativistic cosmology is extended to the case of flow accelerated by pressure. In the description, the entropy and the vorticity are obtained exactly for the barotropic equation of state. In…
In this article, we exhibit certain linking properties of periodic orbits of $C^{1+\alpha}$ flows with positive topological entropy on closed 3-manifolds M. It is shown that any such flow contains a link L of periodic orbits and a horseshoe…
Let $(X,\phi)$ be a compact flow without fixed points. We define the packing topological entropy $h_{\mathrm{top}}^P(\phi,K)$ on subsets of $X$ through considering all the possible reparametrizations of time. For fixed-point free flows, we…
In this paper we found a Lagrangian representation and corresponding Hamiltonian structure for the constant astigmatism equation. Utilizing this Hamiltonian structure and extra conservation law densities we construct a first evolution…
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to…
Deformation of material lines drives transport and dissipation in many industrial and natural flows. Here we report an exact Eulerian formula for the stretching rate of a material line, also known as the topological entropy, in a prototype…