ERGODIC HOMOCLINIC CLASS

We want to introduce a class of points in a closed Riemannian manifold, which is an ergodic component. It is called the ergodic homoclinic class. This class is built on diffeomorphisms on Riemann manifolds, and the definition of ergodic homoclinit class depends on hyperbolic periodic points of diffeomorphisms where the unstable manifolds and stable manifolds of all points in it transversely intersect the stable and unstable man ifolds of points on the orbit of the hyperbolic periodic point respectively. This paper is a summary of the ergodic homoclinic subclass, including its preliminaries, how to prove its ergodicity, its other properties.

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