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

Published online by Cambridge University Press:  05 August 2014

CLAUDIO A. BUZZI ,
TIAGO DE CARVALHO  and
RODRIGO D. EUZÉBIO
CLAUDIO A. BUZZI
Affiliation:
IBILCE-UNESP, CEP 15054-000, S. J. Rio Preto, São Paulo, Brazil email [email protected], [email protected]
TIAGO DE CARVALHO
Affiliation:
FC-UNESP, CEP 17033-360, Bauru, São Paulo, Brazil email [email protected]
RODRIGO D. EUZÉBIO
Affiliation:
IBILCE-UNESP, CEP 15054-000, S. J. Rio Preto, São Paulo, Brazil email [email protected], [email protected]
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 2 , April 2016 , pp. 458 - 469
Copyright
© Cambridge University Press, 2014 

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