Completely Continuous Vector Fields

1984 ◽  
pp. 70-135
Author(s):  
Mark Aleksandrovič Krasnosel’skiéĭ ◽  
Petr Petrovič Zabreĭko
Keyword(s):  
Vector Fields ◽  
Completely Continuous ◽  
Continuous Vector

scholarly journals Quasi-Continuous Vector Fields on RCD Spaces

2020 ◽  
Vol 54 (1) ◽  
pp. 183-211
Author(s):  
Clément Debin ◽  
Nicola Gigli ◽  
Enrico Pasqualetto
Keyword(s):  
Vector Fields ◽  
Continuous Vector

N-DIMENSIONAL CANONICAL CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 239-258 ◽  
Author(s):  
LJ. KOCAREV ◽  
LJ. KARADZINOV ◽  
L. O. CHUA
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Measure Zero ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Continuous Vector ◽  
Linear Vector ◽  
Linear Dynamic ◽  
Canonical Chua’S Circuit

In this paper we present an n-dimensional canonical piecewise-linear electrical circuit. It contains 2n two-terminal elements: n linear dynamic elements (capacitors and inductors), n - 1 linear resistors and one nonlinear (piecewise-linear) resistor. This circuit can realize any prescribed eigenvalue pattern, except for a set of measure zero, associated with (i) any n-dimensional two-region continuous piecewise-linear vector fields and (ii) any n-dimensional three-region symmetric (with respect to the origin) piecewise-linear continuous vector fields. We also proved a theorem that specifies the conditions for a vector field, realized with our canonical circuit, to have two or three equilibrium points.

scholarly journals The Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields

2009 ◽  
Vol 25 (2) ◽  
pp. 495-509 ◽  
Author(s):  
D. P. Demuner ◽  
◽  
M. Federson ◽  
C. Gutierrez
Keyword(s):  
Vector Fields ◽  
Klein Bottle ◽  
Continuous Vector
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