For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. ...

The sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index ...

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize ...

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize ...

For uniformly hyperbolic diffeomorphisms, the large deviation principle was established in the late 1980s by Takahashi, Orey and Pelikan, Kifer, and Young. For quadratic interval maps, the critical point is a serious ...

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such ...

In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the ...

The dynamics of one-dimensional Cahn-Hilliard model is studied. The stationary and particle-type solutions, the bubbles, are perused as a function of initial conditions, boundary conditions, and system size. We characterize the ...

In their pioneer works, Sinai, Bowen, and Ruelle gave a complete description of the thermodynamic formalism of uniformly hyperbolic diffeomorphisms and Holder continuous potentials. In this talk, I'll report on recent ...