A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of connections.
Himpel, Benjamin (2005)
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Himpel, Benjamin (2005)
Geometry & Topology
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Avila, Artur, Viana, Marcelo (2005)
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Saroop Kaul (1987)
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Miroslav Krutina (1989)
Commentationes Mathematicae Universitatis Carolinae
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Alejandro Kocsard (2009)
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Alexander Shnirelman (1999)
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In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...