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Far East Journal of Dynamical Systems

we get some properties of the higher positive prolongation

and higher positive prolongational limit set

It is shown that if

and

then there is an ordinal h such that

For a set

we also discuss two positive prolongations

and two positive prolongational limit sets

and get some relations among them. We also obtain some results about the connectedness of prolongation and prolongational limit set, and a theorem of stability. At last, we discuss dispersive concepts and orbit space.

Far East Journal of Dynamical Systems
Volume 9, Issue 2, Pages 145 - 154 (June 2007)

HIGHER PROLONGATIONS AND DISPERSIVENESS IN DYNAMICAL SYSTEMS
Luo Juan (P. R. China) and Luo Zhimin (P. R. China)

Abstract:
In this paper, we discuss prolongation and prolongational limit set. Let X be a locally compact metric space, for a point

we get some properties of the higher positive prolongation

and higher positive prolongational limit set

It is shown that if

and

then there is an ordinal h such that

For a set

we also discuss two positive prolongations

and two positive prolongational limit sets

Keywords and phrases: prolongation, prolongational limit set, connectedness, stability, dispersiveness.

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