TY - JOUR

T1 - Period-doubling bifurcations in measure-preserving flows

AU - Bountis, T.

AU - Drossos, L.

N1 - Funding Information:
We wish to thank one of the referees for pointing out that Darboux’s theorem may be used to show that all 3-D measure-preserving flows are equivalent under suitable changes of coordinates. We do not think, however, that this is a widely appreciated fact when the coordinates are not canonical, as is the case with the examples treated in this paper. We also wish to thank Dr. R. Quispel, Professor H. Capel and Professor C. Zagouras for many illuminating discus- sions on reversibility, measure-preserving systems and periodic orbits. This work was partially supported by a grant from the Greek Ministry of Industry, Energy and Technology, Division of Research and Technology.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1990/1/29

Y1 - 1990/1/29

N2 - We study period-doubling bifurcations in periodically driven two-dimensional flows, which are measure-preserving. We demonstrate on several examples, that this important bifurcation sequence proceeds very similarly and with the same universal constants, as in the Hamiltonian case of two degrees of freedom. This is explained by the fact that the Poincaré map of our models, upon return to any point of their periodic orbits, is (locally) area-preserving, a result which suggests an equivalence of all measures for such bifurcation phenomena in measure-preserving systems.

AB - We study period-doubling bifurcations in periodically driven two-dimensional flows, which are measure-preserving. We demonstrate on several examples, that this important bifurcation sequence proceeds very similarly and with the same universal constants, as in the Hamiltonian case of two degrees of freedom. This is explained by the fact that the Poincaré map of our models, upon return to any point of their periodic orbits, is (locally) area-preserving, a result which suggests an equivalence of all measures for such bifurcation phenomena in measure-preserving systems.

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U2 - 10.1016/0375-9601(90)90376-Y

DO - 10.1016/0375-9601(90)90376-Y

M3 - Article

AN - SCOPUS:45149136251

VL - 143

SP - 379

EP - 383

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 8

ER -