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27 results on '"Athanassopoulos, Konstantin"'

9. Coherent measures and the unstable manifold of isolated unstable attractors.

Author

Athanassopoulos, Konstantin

Subjects
*ATTRACTORS (Mathematics), *MANIFOLDS (Mathematics), *INVARIANT manifolds, *ORBITS (Astronomy)
Abstract

In this note we give a statistical approximation of the unstable manifold of a connected isolated unstable attractor of a smooth flow using coherent measures relative to it. In the main result we show that almost all orbits in the support of a coherent measure relative to an isolated unstable attractor are contained in its unstable manifold. [ABSTRACT FROM AUTHOR]

Published
2019
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11. Asymtotically stable one-dimensional compact minimal sets

Author

Athanassopoulos, Konstantin

Abstract

It is proved that an asymptotically stable, $1$-dimensional, compact minimal set $A$ of a continuous flow on a locally compact, metric space $X$ is a periodic orbit, if $X$ is locally connected at every point of $A$. So, if the intrinsic topology of the region of attraction of an isolated, $1$-dimensional, compact minimal set $A$ of a continuous flow on a locally compact, metric space is locally connected at every point of $A$, then $A$ is a periodic orbit.

Published
2007

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