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Reconstructing the global dynamics of attractors via the Conley index

100%

McCord C.

Banach Center Publications

1999

tom 47

nr 1

145-156

Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.

The geometry of laminations

100%

Fokkink R. J., Oversteegen L. G.

Fundamenta Mathematicae

1996

tom 151

nr 3

195-207

A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

1 Fokkink R. J.

1 McCord C.

1 Oversteegen L. G.

1 1999

1 1996

Wyniki wyszukiwania

Reconstructing the global dynamics of attractors via the Conley index

The geometry of laminations