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Relatively minimal extensions of topological flows

100%

Mentzen M. K.

Colloquium Mathematicum

2000

tom 84/85

nr 1

51-65

The concept of relatively minimal (rel. min.) extensions of topological flows is introduced. Several generalizations of properties of minimal extensions are shown. In particular the following extensions are rel. min.: distal point transitive, inverse limits of rel. min., superpositions of rel. min. Any proximal extension of a flow Y with a dense set of almost periodic (a.p.) points contains a unique subflow which is a relatively minimal extension of Y. All proximal and distal factors of a point transitive flow with a dense set of a.p. points are rel. min. In the class of point transitive flows with a dense set of a.p. points, distal open extensions are disjoint from all proximal extensions. An example of a relatively minimal point transitive extension determined by a cocycle which is a coboundary in the measure-theoretic sense is given.

Some families of pseudo-processes

100%

Kłapyta J.

Annales Polonici Mathematici

1994-1995

tom 60

nr 1

33-45

We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space $ℝ^m$. The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

1 Kłapyta J.

1 Mentzen M. K.

1 2000

1 1994

Wyniki wyszukiwania

Relatively minimal extensions of topological flows

Some families of pseudo-processes