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Cosymmetry page
A cosymmetry of operator or vector field is a natural cause for existence
of continuous families of solutions of operator equations or equilibria
of dynamical system. The concept of cosymmetry was originally introduced
in Ref.1 by Yudovich
in order to explain the unusual character of the first transition in the
twodimensional problem of filtrational convection [See Ref. 2, Lyubimov,
1975].
Def. Let
be an operator in Hilbert or Euclidian space. An
operator is
called cosymmetry
of L if at each point
an equality holds .
We'll also say that L is a cosymmetry
of ODE in H .
Bibliography

V.I. Yudovich "Cosymmetry, degeneracy of the solution of operator equations,
and the onset of filtrational convection." Mat.Zametki 49, 142 (1991)

D.V.Lyubimov, "Convective motions in a porous medium heated from below,"
Zh.Prikl.Mekh. Tekh. Fiz., No. 2, 131 (1975)

V.I. Yudovich "Cosymmetry and SecondOrder Differential Equations" [in
Russian], deposited at VINITI, 1993, No. 1008V93.

V.I. Yudovich "Cosymmetry and Convection in a Multicomponent Fluid" [in
Russian], deposited at VINITI, 1993, No. 1523V93.

V.I. Yudovich "Secondary cycle of equilibria in a system with cosymmetry,
its creation by bifurcation and impossibility of symmetric treatment of
it". Chaos, Vol.5, No. 2, 1995.
Cosymmetry gallery
Basins of equilibria families
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Page prepared by V.Govorukhin.
Last modified 16 june 1997.
Dep. of Comput.
maths and math. physics, Faculty of Maths and Mechanics, Rostov State
University.