Properties of the Brouwer Degree

2004 ◽  
pp. 55-61
Author(s):  
Robert F. Brown
Keyword(s):  
Brouwer Degree

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.

scholarly journals Higher order averaging theory for finding periodic solutions via Brouwer degree

Nonlinearity ◽  
2014 ◽  
Vol 27 (3) ◽  
pp. 563-583 ◽  
Author(s):  
Jaume Llibre ◽  
Douglas D Novaes ◽  
Marco A Teixeira
Keyword(s):  
Periodic Solutions ◽  
Higher Order ◽  
Averaging Theory ◽  
Brouwer Degree

ASPECT ON BIFURCATION OF ELECTROMAGNETIC VORTEX LINE

2006 ◽  
Vol 21 (17) ◽  
pp. 1369-1376 ◽  
Author(s):  
TAO XU ◽  
HONGLING SU ◽  
GANG ZHOU ◽  
XIWEI HU
Keyword(s):  
Electromagnetic Field ◽  
Critical Points ◽  
Vortex Line ◽  
Singularity Theory ◽  
Brouwer Degree ◽  
Phase Singularity ◽  
Vortex Lines ◽  
Bifurcation Behavior

Vortex lines of electromagnetic field are classified by Hopf index, Brouwer degree in geometry. A mechanism of generation or annihilation of the vortex line is given by method of phase singularity theory. The bifurcation behavior at the critical points is discussed in detail.

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