Wszystkie pola: Nielsen numbers - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A Nielsen theory for intersection numbers
Autorzy:: McCord, Christopher
Powiązania:: https://bibliotekanauki.pl/articles/1205447.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular, NI(f,g) gives a lower bound for the number of points of intersection for all maps homotopic to f and g.
Źródło:: Fundamenta Mathematicae; 1997, 152, 2; 117-150
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Computing Reidemeister classes
Autorzy:: Ferrario, Davide
Powiązania:: https://bibliotekanauki.pl/articles/1205298.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Reidemeister numbers
fixed point theory
Nielsen numbers
Opis:: In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_1(X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.
Źródło:: Fundamenta Mathematicae; 1998, 158, 1; 1-18
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and $C^0$ fixed point sets are the same, by R. E. Greene)
Autorzy:: Schirmer, Helga
Powiązania:: https://bibliotekanauki.pl/articles/1214996.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: transversally fixed maps
minimal and arbitrary fixed point sets
Nielsen fixed point theory
relative and extension Nielsen numbers
Opis:: 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 fixed points in cases where continuous map extensions behave differently from smooth ones. In the appendix it is shown that a subset of a smooth manifold can be realized as the fixed point set of a smooth map in a given homotopy class if and only if it can be realized as the fixed point set of a continuous one. A special case of this result is used in a proof of the paper.
Źródło:: Fundamenta Mathematicae; 1992, 141, 1; 31-59
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem
Autorzy:: Wong, Peter
Powiązania:: https://bibliotekanauki.pl/articles/1215078.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: fixed points
coincidences
roots
Lefschetz number
Nielsen number
Opis:: Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
Źródło:: Fundamenta Mathematicae; 1991-1992, 140, 2; 191-196
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Periodic segments and Nielsen numbers
Autorzy:: Wójcik, Klaudiusz
Powiązania:: https://bibliotekanauki.pl/articles/1341689.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: We prove that the Poincaré map $φ_{(0,T)}$ has at least $N(\tilde h, cl(W_{0} \ W_{0}^{-}) )$ fixed points (whose trajectories are contained inside the segment W) where the homeomorphism $\tilde h$ is given by the segment W.
Źródło:: Banach Center Publications; 1999, 47, 1; 247-252
0137-6934
Pojawia się w:: Banach Center Publications
Dostawca treści:: Biblioteka Nauki

Artykuł

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