An Interdisciplinary Journal

2006, Vol.9, No.4, pp.394-398

Dissipative Dynamical System with Lakes of Vada.
D. W. Serow

The circumstantial evidence of the homoclinic point existence for dissipative diffeomophism on the plane with single inverse saddle fixed point is adduced, that is to say if closure of the unstable manifold of the single inverse saddle fixed point cuts the plane then there subsists homoclinic point. Simple example of the dissipative plane diffeomorphism, such that there exists single fixed point and it is inverse saddle is observed. Closure of unstable manifold of the fixed point is continuum containing in the annual ring and it separates the plane on the some regions! The interior of the invariant set containing in the annual ring with respect to the diffeomorphism is nonempty. Moreover the measure of one is positive.
Key words: homoclinic point, indecomposable continuum, lakes of Vada

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