Geodesic
On the possibility of implementing the Landau--Hopf scenario of transition to turbulence in the generalized model ``multiplier-accelerator''
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 39-49.

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In this paper, we consider two boundary-value problems for the multiplier-accelerator model taking into account spatial effects. We show that, under an appropriate choice of the control parameter, invariant tori of increasing dimensions arise in both boundary-value problems and the invariant torus of the highest dimension is stable. Our results are based on such methods of the theory of dynamical systems with infinite-dimensional phase spaces as the method of integral manifolds, the Poincaré method of normal forms, and F. Takens' plan for implementing the Landau—Hopf scenario as a cascade of Andronov—Hopf bifurcations. For solutions that belong to invariant tori, we obtain asymptotic formulas.
Keywords: Landau–Hopf scenario, normal form, multiplier-accelerator, boundary-value problem.
Mots-clés : stable invariant torus, cascade of bifurcations 
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A. N. Kulikov; D. A. Kulikov. On the possibility of implementing the Landau--Hopf scenario of transition to turbulence in the generalized model ``multiplier-accelerator''. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 39-49. http://geodesic.mathdoc.fr/item/INTO_2021_203_a3/

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