Decay of geometry for Fibonacci critical covering maps of the circle
Dependence of hidden attractors on non-linearity and Hamilton energy in a class of chaotic system
Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical...
Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation
We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup does exist for any bounded ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.
Differentiable semiflows for differential equations with state-dependent delays.
Dissipative dynamics of reaction diffusion equations in
Dynamical properties for a relaxation scheme applied to a weakly damped non local nonlinear Schrödinger equation.
Dynamics of a Lotka-Volterra map
Given the plane triangle with vertices (0,0), (0,4) and (4,0) and the transformation F: (x,y) ↦ (x(4-x-y),xy) introduced by A. N. Sharkovskiĭ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior...
Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller...
Dynamics of stochastic approximation algorithms