On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphisms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F17%3AA180197L" target="_blank" >RIV/61988987:17610/17:A180197L - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/etds.2015.129" target="_blank" >http://dx.doi.org/10.1017/etds.2015.129</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/etds.2015.129" target="_blank" >10.1017/etds.2015.129</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphisms

Popis výsledku v původním jazyce

We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose h is an orientation preserving homeomorphism,X is a one-dimensional nonseparating plane continuum and C is a component of X intersection h(X). If there is a c in C such that its entire forward or backward orbit is contained in C then then C also contains a fixed point of h. Consequently if there are n components of X intersection h(X), each of which contains a periodic orbit then h has at least n fixed points in X. Our approach is based on Morton Brown's short proof of the result of Cartwright and Littlewood. In addition, making use of a linked periodic orbits theorem of Bonino we also prove a counterpart of the aforementioned result for orientation reversing homeomorphisms,that guarantees a 2-periodic orbit in X.

Název v anglickém jazyce

On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphisms

Popis výsledku anglicky

We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose h is an orientation preserving homeomorphism,X is a one-dimensional nonseparating plane continuum and C is a component of X intersection h(X). If there is a c in C such that its entire forward or backward orbit is contained in C then then C also contains a fixed point of h. Consequently if there are n components of X intersection h(X), each of which contains a periodic orbit then h has at least n fixed points in X. Our approach is based on Morton Brown's short proof of the result of Cartwright and Littlewood. In addition, making use of a linked periodic orbits theorem of Bonino we also prove a counterpart of the aforementioned result for orientation reversing homeomorphisms,that guarantees a 2-periodic orbit in X.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ERGOD THEOR DYN SYST

ISSN

0143-3857

e-ISSN

—

Svazek periodika

37

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

1815-1824

Kód UT WoS článku

000407181600003

EID výsledku v databázi Scopus

2-s2.0-84957803488