Limitation of Perpetual Points for Confirming Conservation in
Dynamical Systems
Sajad Jafari and Fahimeh Nazarimehr
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
sajadjafari@aut.ac.ir
J. C. Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA
Sayed Mohammad Reza Hashemi Golpayegani
Biomedical Engineering Department,
Amirkabir University of Technology,
Tehran 15875-4413, Iran
Received May 23, 2015
ABSTRACT
Perpetual Points (PPs) have been
introduced as an interesting new topic in nonlinear dynamics,
and there is a hypothesis that these points can determine
whether a system is dissipative or not. This paper demonstrates
that this hypothesis is not true since there are
counterexamples. Furthermore, we explain that it is impossible
to determine dissipation of a system based only on the structure
of the system and its equations.
Ref: S. Jafari, F. Nazarimehr, J. C.
Sprott, and S. M. R. H. Golpayegani, International Journal
of Bifurcation and Chaos 25
1550182 (2015)
The complete paper is available in
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