2. Topological degree, rotation, and fixed points of multivalued mappings in finite-dimensional spaces

1987 ◽  
Vol 39 (3) ◽  
pp. 2786-2790
Keyword(s):  
Fixed Points ◽  
Topological Degree ◽  
Multivalued Mappings ◽  
Finite Dimensional

scholarly journals Fixed Points for Multivalued Mappings and the Metric Completeness

2009 ◽  
Vol 2009 (1) ◽  
pp. 972395 ◽  
Author(s):  
S Dhompongsa ◽  
H Yingtaweesittikul
Keyword(s):  
Fixed Points ◽  
Multivalued Mappings

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

Fixed Points and Topological Degree in Nonlinear Analysis (Jane Cronin)

SIAM Review ◽  
1965 ◽  
Vol 7 (1) ◽  
pp. 141-143
Author(s):  
F. S. van Vleck
Keyword(s):  
Fixed Points ◽  
Nonlinear Analysis ◽  
Topological Degree

Computing the Number of Fixed Joints on Poincare Map in Nonlinear Mathieu Equation

1993 ◽  
Author(s):  
Hisato Fujisaka ◽  
Chikara Sato
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Numerical Method ◽  
Topological Degree ◽  
Poincaré Map ◽  
Mathieu Equation ◽  
Time Varying ◽  
Poincare Map ◽  
Newton's Iteration ◽  
Combined Use

Abstract A numerical method is presented to compute the number of fixed points of Poincare maps in ordinary differential equations including time varying equations. The method’s fundamental is to construct a map whose topological degree equals to the number of fixed points of a Poincare map on a given domain of Poincare section. Consequently, the computation procedure is simply computing the topological degree of the map. The combined use of this method and Newton’s iteration gives the locations of all the fixed points in the domain.

scholarly journals On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

2019 ◽  
Vol 22 (6) ◽  
pp. 1089-1099
Author(s):  
Motoko Kato
Keyword(s):  
Fixed Points ◽  
Topological Dimension ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Thompson’S Group ◽  
Simple Action ◽  
Cube Complexes

Abstract We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson’s group T and various generalizations of Thompson’s group V have global fixed points when they act semi-simply on finite-dimensional complete CAT(0) spaces, while it is known that T and V act properly on infinite-dimensional CAT(0) cube complexes.

Seiberg-Witten invariants, the topological degree and wall crossing formula

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Maciej Starostka
Keyword(s):  
Simple Proof ◽  
Topological Degree ◽  
Witten Invariant ◽  
Homotopy Invariance ◽  
Finite Dimensional ◽  
Wall Crossing ◽  
Wall Crossing Formula

AbstractFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.

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