Chapter 3 Conformal equivalence and the Poincaré index

1996 ◽  
Keyword(s):  
Poincaré Index ◽  
Conformal Equivalence ◽  
Poincare Index

scholarly journals Poincaré index and the volume functional of unit vector fields on punctured spheres

2019 ◽  
Vol 161 (3-4) ◽  
pp. 487-499
Author(s):  
Fabiano G. B. Brito ◽  
André O. Gomes ◽  
Icaro Gonçalves
Keyword(s):  
Vector Fields ◽  
Unit Vector ◽  
Volume Functional ◽  
Poincaré Index ◽  
Unit Vector Fields ◽  
Poincare Index

scholarly journals Poincaré index of plane polynomial fields of third and fourth degree

2019 ◽  
Vol 55 (1) ◽  
pp. 22-31
Author(s):  
P. P. Zabreiko ◽  
A. V. Krivko-Krasko
Keyword(s):  
Singular Point ◽  
Greatest Common Divisor ◽  
Fourth Degree ◽  
Real Zeros ◽  
Poincaré Index ◽  
Poincare Index

The conditions of isolation of a zero singular point of plane polynomial fields of third and fourth degree are considered in terms of the coefficients of the components of these fields. The isolation conditions depend on the greatest common divisor of the components of polynomial fields: in some cases only on its degree, and in some cases, additionally, on the presence of nonzero real zeros. The reasoning, which allows one to write out the isolation conditions, is based on the concept of the resultant and subresultants of components of plane polynomial fields. If the zero singular point is isolated, its index is calculated through the values of subresultants and coefficients of components.

scholarly journals An index for Brouwer homeomorphisms and homotopy Brouwer theory

2015 ◽  
Vol 37 (2) ◽  
pp. 572-605
Author(s):  
FRÉDÉRIC LE ROUX
Keyword(s):  
Fixed Point ◽  
Poincaré Index ◽  
Poincare Index

We use the homotopy Brouwer theory of Handel to define a Poincaré index between pairs of orbits for an orientation-preserving fixed-point-free homeomorphism of the plane. Furthermore, we prove that this index is almost additive.

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