scholarly journals Large KAM Tori for Quasi-linear Perturbations of KdV

2021 ◽  
Author(s):  
Massimiliano Berti ◽  
Thomas Kappeler ◽  
Riccardo Montalto
Keyword(s):  
Kam Tori ◽  
Linear Perturbations

The Einstein pseudo-tensor and the flux integral for perturbed static space-times

1991 ◽  
Vol 435 (1895) ◽  
pp. 645-657 ◽  
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Second Variation ◽  
Common Procedure ◽  
Static Vacuum ◽  
Linear Perturbations ◽  
Maxwell Space ◽  
The Common ◽  
Static Space

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

Linear perturbations of the fractional Yamabe problem on the minimal conformal infinity

2021 ◽  
Vol 29 (2) ◽  
pp. 363-407
Author(s):  
Shengbing Deng ◽  
Seunghyeok Kim ◽  
Angela Pistoia
Keyword(s):  
Yamabe Problem ◽  
Linear Perturbations

Kam Tori for Modulated Symplectic Maps

1994 ◽  
pp. 140-153
Author(s):  
Armando Bazzani
Keyword(s):  
Kam Tori ◽  
Symplectic Maps

scholarly journals A Possible Mechanism for the Kam Tori Breakdown

1999 ◽  
pp. 372-376 ◽  
Author(s):  
Guido Gentile ◽  
Vieri Mastropietro
Keyword(s):  
Kam Tori

scholarly journals Perturbation dynamics in Keplerian flow under external stochastic forcing

2020 ◽  
Vol 492 (4) ◽  
pp. 5366-5376 ◽  
Author(s):  
D N Razdoburdin
Keyword(s):  
Reynolds Number ◽  
Angular Momentum ◽  
Momentum Transfer ◽  
Reynolds Numbers ◽  
Stochastic Forcing ◽  
Stochastic Force ◽  
Angular Momentum Transfer ◽  
Linear Perturbations ◽  
Average Angular Momentum ◽  
Astrophysical Flows

ABSTRACT We investigate the dynamics of linear perturbations in Keplerian flow under external stochastic force. To abstract from the details of flow structure and boundary conditions, we consider the problem in the shearing box approximation. An external force is assumed to have zero mean, even so, induced perturbations form a steady state, which provides angular momentum transfer to the periphery of the flow. The most effective scenario is based on the transient amplification of induced vortices with the following emission of a shearing sound wave, wherein the maximum of the flux linearly depends on Reynolds number. Thus such a mechanism is significant for astrophysical flows, for which enormous Reynolds numbers are typical. At the same time, addressing the problem analytically, we find that for incompressible fluid in the shearing box approximation stochastic forcing does not lead to average angular momentum transfer. Thus the compressibility of the fluid plays an important role here, and one cannot neglect it.

scholarly journals Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 47 ◽  
Author(s):  
Davor Dragičević ◽  
Ciprian Preda
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Complete Characterization ◽  
Skew Product ◽  
Linear Perturbations

For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations.

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