A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, bot...A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.展开更多
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essentia...The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.展开更多
文摘A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.
基金supported by the National Natural Science Foundation of China(Grant Nos.11073012,11078001 and 11003008)the Qing Lan Project(Jiangsu Province)the National Basic Research Program of China(Grant Nos.2013CB834103 and 2013CB834904)
文摘The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.
