Solitary Waves as Fixed Points of Infinite-Dimensional Maps in an Optical Bistable Ring Cavity

1983 ◽  
Vol 51 (2) ◽  
pp. 75-78 ◽  
Author(s):  
D. W. Mc Laughlin ◽  
J. V. Moloney ◽  
A. C. Newell
Keyword(s):  
Fixed Points ◽  
Solitary Waves ◽  
Ring Cavity ◽  
Infinite Dimensional

Solitary waves as fixed points of infinite‐dimensional maps for an optical bistable ring cavity: Analysis

1988 ◽  
Vol 29 (1) ◽  
pp. 63-85 ◽  
Author(s):  
H. Adachihara ◽  
D. W. McLaughlin ◽  
J. V. Moloney ◽  
A. C. Newell
Keyword(s):  
Fixed Points ◽  
Solitary Waves ◽  
Ring Cavity ◽  
Infinite Dimensional

A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Mann Iteration ◽  
Infinite Dimensional ◽  
Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

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.

INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS

2007 ◽  
Vol 17 (12) ◽  
pp. 4261-4272 ◽  
Author(s):  
ZBIGNIEW GALIAS ◽  
PIOTR ZGLICZYŃSKI
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Discrete Dynamical Systems ◽  
Krawczyk Operator ◽  
Infinite Dimensional ◽  
Dispersal Model ◽  
Period 2 ◽  
Existence Of Zeros

In this work, we introduce the Krawczyk operator for infinite dimensional maps. We prove two properties of this operator related to the existence of zeros of the map. We also show how the Krawczyk operator can be used to prove the existence of periodic orbits of infinite dimensional discrete dynamical systems and for finding all periodic orbits with a given period enclosed in a specified region. As an example, we consider the Kot–Schaffer growth-dispersal model, for which we find all fixed points and period-2 orbits enclosed in the region containing the attractor observed numerically.

scholarly journals Convergence Theorems for Accretive Operators with Nonlinear Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yan-Lai Song ◽  
Lu-Chuan Ceng
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Recent Literature ◽  
Common Element ◽  
Inclusion Problem ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of strict pseudocontractions in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating these common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Further, we consider the problem of finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a strict pseudocontractions.

Fixed Points and Chaotic Dynamics of an Infinite Dimensional Map

2020 ◽  
pp. 137-186
Author(s):  
J V Moloney ◽  
H Adachihara ◽  
D W McLaughlin ◽  
A C Newell
Keyword(s):  
Fixed Points ◽  
Chaotic Dynamics ◽  
Infinite Dimensional

FOURTH-ORDER NUMERICAL METHODS FOR THE COUPLED KORTEWEG–DE VRIES EQUATIONS

2015 ◽  
Vol 56 (3) ◽  
pp. 275-285
Author(s):  
I. A. KOROSTIL ◽  
S. R. CLARKE
Keyword(s):  
Numerical Methods ◽  
Fixed Points ◽  
Solitary Waves ◽  
Fourth Order ◽  
Test Problems ◽  
Integral Invariants ◽  
De Vries

We compare six fixed-stepsize fourth-order numerical methods for a number of test problems described by a system of coupled Korteweg–de Vries equations. Particular attention is paid to the ability of these methods to preserve fixed points (solitary waves) and the invariants of the system, and establishing to what extent the conservation of integral invariants is indicative of the solution error for these methods.

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