scholarly journals On Poincaré-Bendixson Theorem and non-trivial minimal sets in planar nonsmooth vector fields

2018 ◽  
Vol 62 ◽  
pp. 113-131 ◽  
Author(s):  
Claudio A. Buzzi ◽  
Tiago Carvalho ◽  
Rodrigo D. Euzébio
Keyword(s):  
Vector Fields ◽  
Minimal Sets

Chaos and non-trivial minimal sets in discontinuous vector fields

2015 ◽  
Author(s):  
Claudio A. Buzzi ◽  
Rodrigo D. Euzébio ◽  
Tiago De Carvalho
Keyword(s):  
Vector Fields ◽  
Minimal Sets ◽  
Discontinuous Vector Fields

scholarly journals Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

2014 ◽  
Vol 36 (2) ◽  
pp. 458-469 ◽  
Author(s):  
CLAUDIO A. BUZZI ◽  
TIAGO DE CARVALHO ◽  
RODRIGO D. EUZÉBIO
Keyword(s):  
Vector Fields ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Deterministic Chaos ◽  
Piecewise Smooth ◽  
Smooth Vector ◽  
Minimal Sets ◽  
Piecewise Smooth Vector Fields

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

On the Minimal Sets of Non-Singular Vector Fields

1966 ◽  
Vol 84 (3) ◽  
pp. 529 ◽  
Author(s):  
F. Wesley Wilson
Keyword(s):  
Vector Fields ◽  
Singular Vector ◽  
Minimal Sets

scholarly journals On the birth of minimal sets for perturbed reversible vector fields

2011 ◽  
Vol 31 (3) ◽  
pp. 763-777
Author(s):  
Jaume Llibre ◽  
◽  
Ricardo Miranda Martins ◽  
Marco Antonio Teixeira ◽  
Keyword(s):  
Vector Fields ◽  
Minimal Sets
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