Discrete & Continuous Dynamical Systems
September 2020 , Volume 40 , Issue 9
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We study an interval exchange transformation of
Volume entropy is an important invariant of metric graphs as well as Riemannian manifolds. In this note, we calculate the change of volume entropy when an edge is added to a metric graph or when a vertex and edges around it are added. In the second part, we estimate the value of the volume entropy which can be used to suggest an algorithm for calculating the persistent volume entropy of graphs.
In this paper, we find some general and efficient sufficient conditions for the exponential convergence
In this paper, we study the relations between curvature and Anosov geodesic flow. More specifically, we prove that when the geodesic flow of a complete manifold without conjugate points is of the Anosov type, then the average of the sectional curvature in tangent planes along geodesics is negative and uniformly away from zero. Moreover, if a surface has no focal points, then the latter condition is sufficient to obtain that the geodesic flow is of Anosov type.
By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations.
A family of dispersive equations is considered, which links a higher-dimensional Benjamin-Ono equation and the Zakharov-Kuznetsov equation. For these fractional Zakharov-Kuznetsov equations new well-posedness results are proved using transversality and time localization to small frequency dependent time intervals.
In this paper one extends results of Bendixson [
In this paper, we study an analytic curve
We study regularity criteria for the
We develop a renormalization group approach to the problem of reducibility of quasi-periodically forced circle flows. We apply the method to prove a reducibility theorem for such flows.
With the same techniques, we establish polynomial mixing of all orders under the additional assumption of
In this paper we shall establish some Liouville theorems for solutions bounded from below to certain linear elliptic equations on the upper half space. In particular, we show that for
We will extend a recent result of B. Choi, P. Daskalopoulos and J. King [
This paper is concerned with the time periodic problem to a coupled chemotaxis-fluid model with porous medium diffusion
It is established multiplicity of solutions for critical quasilinear Schrödinger equations defined in the whole space using a linking structure. The main difficulty comes from the lack of compactness of Sobolev embedding into Lebesgue spaces. Moreover, the potential is bounded from below and above by positive constants. In order to overcome these difficulties we employ Lions Concentration Compactness Principle together with some fine estimates for the energy functional restoring some kind of compactness.
We prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density profile is supposed to be increasing in depth and linearized around a stable state. Moreover if the Froude number tends to zero we prove that such system converges (strongly) to a two-dimensional, stratified Navier-Stokes equations with full diffusivity. No smallness assumption is considered on the initial data.
In this work, the Cauchy problem for the semilinear Moore – Gibson – Thompson (MGT) equation with power nonlinearity
In this paper, we consider the following equivariant defocusing Chern-Simons-Schrödinger system,
For a nonautonomous linear system with nonuniform contraction, we construct a topological conjugacy between this system and an unbounded nonlinear perturbation. This topological conjugacy is constructed as a composition of homeomorphisms. The first one is set up by considering the fact that linear system is almost reducible to diagonal system with a small enough perturbation where the diagonal entries belong to spectrum of the nonuniform exponential dichotomy; and the second one is constructed in terms of the crossing times with respect to unit sphere of an adequate Lyapunov function associated to the linear system.
In this paper, we consider the following critical quasilinear equation with Hardy potential:
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