The Kronecker Index and the Brouwer Degree

2020 ◽  
pp. 1-76
Author(s):  
George Dinca ◽  
Jean Mawhin
Keyword(s):  
Brouwer Degree ◽  
Kronecker Index

A Simple Approach to Brouwer Degree Based on Differential Forms

2004 ◽  
Vol 4 (4) ◽  
Author(s):  
Jean Mawhin
Keyword(s):  
Differential Forms ◽  
Simple Approach ◽  
Elementary Level ◽  
Brouwer Degree ◽  
Homotopy Invariance ◽  
Unpublished Result ◽  
Kronecker Index

AbstractWe present Heinz’ approach to Brouwer degree in a simpler, shorter and better motivated way. We link it to Kronecker index, use the language of differential forms at an elementary level, and prove the homotopy invariance using an unpublished result of Tartar.

Brouwer Degree

2014 ◽  
pp. 57-61
Author(s):  
Robert F. Brown
Keyword(s):  
Brouwer Degree

scholarly journals Computing the Brouwer degree in $R\sp{2}$

1973 ◽  
Vol 27 (121) ◽  
pp. 133-133
Author(s):  
P. J. Erdelsky
Keyword(s):  
Brouwer Degree

Degree, quaternions and periodic solutions

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190378
Author(s):  
Jean Mawhin
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Topological Degree ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Brouwer Degree ◽  
Homogeneous Polynomials ◽  
Theme Issue ◽  
Existence And Multiplicity

The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

scholarly journals Brouwer degree, equivariant maps and tensor powers

1998 ◽  
Vol 3 (3-4) ◽  
pp. 401-409 ◽  
Author(s):  
Z. Balanov ◽  
W. Krawcewicz ◽  
A. Kushkuley
Keyword(s):  
Differential Equations ◽  
Faithful Representation ◽  
Brouwer Degree ◽  
Symmetric Powers ◽  
Equivariant Maps ◽  
Tensor Powers

A construction of equivariant maps based on factorization through symmetric powers of a faithful representation is presented together with several examples of related equivariant maps. Applications to differential equations are also discussed.

scholarly journals On algebraic problems behind the Brouwer degree of equivariant maps

2020 ◽  
Vol 549 ◽  
pp. 45-77
Author(s):  
Zalman Balanov ◽  
Mikhail Muzychuk ◽  
Hao-pin Wu
Keyword(s):  
Brouwer Degree ◽  
Equivariant Maps

TOPOLOGICAL SOLUTION OF BOHMIAN QUANTUM MECHANICS

2009 ◽  
Vol 24 (06) ◽  
pp. 453-461 ◽  
Author(s):  
XUGUANG SHI ◽  
MING YU ◽  
YISHI DUAN
Keyword(s):  
Quantum Mechanics ◽  
Particle System ◽  
World Line ◽  
Zero Point ◽  
Current Theory ◽  
Brouwer Degree ◽  
Topological Current ◽  
The World ◽  
Bohmian Quantum Mechanics ◽  
De Broglie Bohm

The topological solutions of the De Broglie–Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ϕ-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

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