On existence of global attractors of foliations with transverse linear connections |
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| Affiliation: | National Research University Higher School of Economics, Laboratory of Dynamical Systems and Applications, 25/12, Bolshaya Pecherskaya St., Nizhny Novgorod, 603155, Russia |
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| Abstract: | The existence problem for attractors of foliations with transverse linear connection is investigated. In general foliations with transverse linear connection do not admit attractors. Sufficient conditions are found for the existence of a global attractor that is a minimal set. An application to transversely similar pseudo-Riemannian foliations is obtained. The global structure of transversely similar Riemannian foliations is described. Different examples are constructed. |
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| Keywords: | Foliation Attractor Minimal set Foliation with transverse linear connection Global attractor |
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