TITLE:
Unstable quasi-periodic solutions for the 2-D Poiseuille problem

AUTHORS:
Pablo S. Casas^(1), Angel Jorba^(2)

(1) pablo@casas.upc.es
Departament de Matematica Aplicada I,
Universitat Politecnica de Catalunya,
Diagonal 647, 08028 Barcelona (Spain).

(2) angel@maia.ub.es
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona (Spain).

ABSTRACT:
In the 2-D Poiseuille problem arise several Hopf bifurcations on the
branch of secondary flows, which in turn bifurcate from the laminar
solution. We analyze the first Hopf bifurcation of secondary flows
where the period on time of the bifurcated solution is $O(1000)$.
Previous calculations of these solutions show that the Hopf
bifurcation is subcritical and thus the bifurcated quasi-periodic
solutions are locally stable. By improving the precision of the
numerical approximation we obtain unstable quasi-periodic flows given
rise to a supercritical Hopf bifurcation.
