An Interdisciplinary Journal

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

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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Last updated: *January 4, 2007*