# 一类两点异宿环中含马蹄的充分条件A Sufficient Condition of a Class of Two Points Heteroclinic Loop Having Horseshoe

Abstract: In this paper, for a class of three-dimensional autonomous vector field which has heteroclinic loop containing two hyperbolic fixed points, a saddle point and a saddle-focus point, we structure the Poincare map by choosing appropriate local coordinate system and using the flow of linearized vector field inside the small neighborhood of the two fixed points and present a sufficient condition of the Poincare map possessing a countable infinite horseshoes.

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