Bifurcations of Invariant Tori in Second-Order Quasilinear Evolution Equations in Hilbert Spaces and Scenarios of Transition to Turbulence

In this paper, we consider second-order quasilinear differential equations in a separable Hilbert space for which the well-known Landau–Hopf scenario of transition to turbulence can be realized. We prove increasing of the control parameter leads to the consecutive appearance of invariant tori of inc...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-04, Vol.262 (6), p.809-816
Main Author: Kulikov, A. N.
Format: Article
Language:English
Subjects:
Analysis
Asymptotic methods
Bifurcations
Canonical forms
Differential equations
Dynamical systems
Hilbert space
Initial conditions
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Toruses
Turbulence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider second-order quasilinear differential equations in a separable Hilbert space for which the well-known Landau–Hopf scenario of transition to turbulence can be realized. We prove increasing of the control parameter leads to the consecutive appearance of invariant tori of increasing dimensions. In this case, the invariant torus of the largest possible dimension appears to be attractive. The results are obtained by using methods of the qualitative theory of dynamical systems with an infinite-dimensional space of initial conditions: the method of integral manifolds, the theory of normal forms, and also asymptotic methods of analysis of dynamical systems.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05859-z