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Equivariant Morse equation

100%

Styborski M.

Open Mathematics

2012

tom 10

nr 6

2138-2159

The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by .x = −∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.

Degree of T-equivariant maps in ℝⁿ

63%

Janczewska J., Styborski M.

Banach Center Publications

2007

tom 77

nr 1

147-159

A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution $T:ℝ^p ⊕ ℝ^q → ℝ^p ⊕ ℝ^q$ given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps $f,g:(ℝⁿ,S^{n-1}) → (ℝⁿ,ℝⁿ∖{0})$ are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

2 Styborski M.

1 Janczewska J.

1 2012

1 2007

Wyniki wyszukiwania

Equivariant Morse equation

Degree of T-equivariant maps in ℝⁿ