Displaying similar documents to “Multiple perturbed solutions near nondegenerate manifolds of solutions”

Nielsen theory of transversal fixed point sets (with an appendix: C ∞ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

An intrinsic definition of the Colombeau generalized functions

Jiří Jelínek (1999)

Commentationes Mathematicae Universitatis Carolinae

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A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a 𝒞 ∞ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.

The semi-index product formula

Jerzy Jezierski (1992)

Fundamenta Mathematicae

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We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| ( f b , g b : p - 1 ( b ) ∩ A ) to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and N ( f b , g b ) .