Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Fixed points of n-valued multimaps of the circle

Brown R. F.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 2

153-162

A multifunction φ: X → Y is n-valued if φ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n- valued multimaps φ: S1 → S1 are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(φ) of an n-valued φ: S1 → S1 of degree d equals \n - d\ and φ is homotopic to an n-valued power map that has exactly \n - d\ fixed points. Thus the Wecken property, that Schirmer established for manifolds of dimension at least three, also holds for the circle. An n-valued multimap φ: S1 → S1 of degree d splits into n selfmaps of S1 if and only if d is a multiple of n.