2019-08-20T21:26:58Z
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oai:oa.upm.es:21583
2016-10-26T09:22:24Z
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A generic, hard transition to chaos
López-Rebollal, Óscar
Sanmartín Losada, Juan Ramón
Physics
Aeronautics
A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive
values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional
parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an
invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic
structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic
flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators
in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed
E.T.S.I. Aeronáuticos (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
1995
info:eu-repo/semantics/article
Article
Physica D, ISSN 0167-2789, 1995, Vol. 89
PeerReviewed
application/pdf
eng
info:eu-repo/semantics/openAccess
http://oa.upm.es/21583/