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An Algorithm for Computing a New Normal Form for Dynamical Systems

2000
*
Journal of symbolic computation
*

We propose in this paper a new

doi:10.1006/jsco.1999.0305
fatcat:szginflozzchrddcsrdvma2ueq
*normal**form**for**dynamical**systems*or vector fields which improves the classical*normal**forms*in the sense that it is a further reduction of the classical*normal**forms*. ... As a particular case, if the matrix of the*linear*part is a companion matrix then we reduce the*dynamical**system*to a single differential equation. ... Using the*Carleman**linearization*procedure and a Frobenius basis in H k we introduced in Chen and Della Dora (1999a) a*rational*method*for*the*normal**form*of any*dynamical**system*. ...##
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Page 8025 of Mathematical Reviews Vol. , Issue 2003j
[page]

2003
*
Mathematical Reviews
*

Summary: “In this paper, motivated

*by*the restrictive conditions required to obtain an exact chained*form*, we propose a quadratic*normal**form*around a one-dimensional equilibrium submanifold*for**systems*... Poincaré*normal**form**for*a class of driftless*systems*in a one-dimensional submanifold neighborhood. (English summary) Math. Control Signals*Systems*15 (2002), no. 3, 256-274. ...##
###
Page 3490 of Mathematical Reviews Vol. , Issue 2004d
[page]

2004
*
Mathematical Reviews
*

and restricted smooth state feedback, a gen- eralized

*normal**form*called the p-*normal**form*, which includes the Brunovsky canonical*form*and feedback linearizable*systems*in a lower-triangular*form*as ... Summary: “*For*a class of*dynamical**systems*, with uncertain non-*linear*terms considered as unknown inputs, we give sufficient conditions*for*observability. ...##
###
Page 981 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

Xue Min Li (PRC-SHDN; Jinan)
2002b:34010 34A25 37G05
Chen, Guoting (F-LILL; Villeneuve d’Ascq);
Della Dora, Jean (F-GREN-LM; Grenoble)

*Rational**normal**form**for**dynamical**systems**by**Carleman**linearization*... They recall the so called*Carleman**Linearization*, that is they consider the action of the derivative D in the infinite-dimensional space generated*by*monomials of the*form*x® = x}"'x;?...xf". ...##
###
Page 2133 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

They also provide

*Carleman*estimates and global*For*the web version of Mathematical Reviews, see http: //www.ams .org/mathscinet ... The authors study controllability properties of a class of*linear*control*systems*of the*form*x(t) = Ax(t)+ Bu(t), 1>0, x(t)eE X, u(t) € U, where X, U are non-reflexive Banach spaces. ...##
###
Exact Solutions of Discrete Kinetic Models and Stationary Problems for the Plane Broadwell Model

1996
*
Mathematical methods in the applied sciences
*

*for*a non-empty class of solutions p(x,t) and u(x,t) of the

*linear*

*system*(5) . ... The approach based on the Poincare

*normal*

*form*method (

*Carleman*model) We consider here the

*Carleman*equations in dimensionless

*form*I a a -+- at ax where f,(x,t) a a f= 1 ! ...

##
###
Further Reductions of Normal Forms for Dynamical Systems

2000
*
Journal of Differential Equations
*

*For*

*dynamical*

*systems*of dimensions 2 and 3 we give an algorithm that leads to interesting finite order

*normal*

*forms*which are optimal (or unique) with respect to equivalence

*by*formal near identity transformations ... We propose in this paper a method

*for*obtaining a significant refinement of

*normal*

*forms*

*for*

*dynamical*

*systems*or vector fields, with concrete and interesting applications. ... We take v=w=0 in the following, since we are looking

*for*

*rational*

*normal*

*forms*. We study further reductions of

*systems*with the given

*linear*part

*by*near identity transformations. ...

##
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Page 6923 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

Hartje Kriete (D-GTN; Gottingen)
98k:30032 30D05 58F23
Gong, Zhimin (PRC-FUDAN-IM; Shanghai);
Ren, Fuyao (PRC-FUDAN-IM; Shanghai)
A random

*dynamical**system**formed**by*infinitely many functions. ... This result, which the author proves*for**rational*functions R(z), was proved*for*polynomials P(z)*by*A. Eremenko and G. M. Levin [Ukrain. Mat. ...##
###
Reducing nonlinear dynamical systems to canonical forms

2018
*
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
*

The drawback of this diversity is that it has prevented the construction of a theoretical apparatus as powerful as the one developed from

doi:10.1098/rsta.2017.0384
pmid:29891502
fatcat:43yov5yu7fazfmvvidorgurali
*linear*algebra*for**linear**dynamical**systems*of*form*(2.1). ... as a comparison, let us write down the corresponding abstract Lie algebra*for**linear**systems*of*form*(2.1). ...##
###
Page 1917 of Mathematical Reviews Vol. 57, Issue 5
[page]

1979
*
Mathematical Reviews
*

*For*a

*system*of

*linear*equations characterizing the initial mixed boundary-value problems of thermoelastic shells, a uniqueness theorem is obtained without the use of a definiteness assumption

*for*the ... The Laplace trans-

*form*is used and the general solution of the equation of motion corresponding to general

*dynamic*loads is obtained. ...

##
###
Page 8 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

Gaiko], Limit cycle bifurcations in polynomial models of

*dynamical*sys- tems (525-534); Katrin Gelfert, Lower estimates of the topological entropy*for**dynamical**systems*on Riemannian manifolds (535 543 ... Vasil’ev], Obtaining the self-similar asymptotics of solutions to the Navier-Stokes equations*by*power geometry (93-101); Shuji Watanabe, A generalized Fourier trans-*form*(103-113); Anatoly A. ...##
###
Data-driven modeling and control of large-scale dynamical systems in the Loewner framework
[article]

2021
*
arXiv
*
pre-print

This is a data-driven approach, applicable to large-scale

arXiv:2108.11870v1
fatcat:o2anvfh4kncjravkvto2gxfw4y
*systems*, which was originally developed*for*applications to*linear*time-invariant*systems*. ... In recent years, this method has been extended to a number of additional more complex scenarios, including*linear*parametric or nonlinear*dynamical**systems*. ...*For*recent tutorial papers on LF applied to*linear**dynamical**systems*, we refer the reader to [7, 33] . ...##
###
Rational function approximations in the numerical solution of Cauchy-type singular integral equations

1985
*
Computers and Mathematics with Applications
*

*Rational*function approximations in the solution of the dommant equation results in a

*linear*algebraic

*system*which possesses blockdiagonal structure. ... Hence. approximations

*by*

*rational*functions IS feasible. ... Section 3 outlines the basic strategy of the

*rational*function method

*for*the dominant equation and brings out the desirable block-diagonal structure of the

*linear*

*system*of equations. ...

##
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A modified particle method for semilinear hyperbolic systems with oscillatory solutions

2004
*
Methods and Applications of Analysis
*

We introduce a modified particle method

doi:10.4310/maa.2004.v11.n4.a8
fatcat:wjzmd7f43rce7jserh3pcgwh6m
*for*semi-*linear*hyperbolic*systems*with highly oscillatory solutions. ... We prove the convergence of the modified particle method essentially independent of the small scale*for*the variable coefficient*Carleman*model. ... Hou was supported in part*by*NSF under the NSF FRG grant DMS-0353838 and ITR Grant ACI-0204932. ...##
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Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems

2002
*
Applied Numerical Mathematics
*

The surge of interest was triggered

doi:10.1016/s0168-9274(02)00116-2
fatcat:kxudva7urvelnbogve5a27uywy
*by*the pressing need*for*efficient numerical techniques*for*simulations of extremely large-scale*dynamical**systems*arising from circuit simulation, structural*dynamics*... In this paper, we begin with a tutorial of a Lanczos process based Krylov subspace technique*for*reduced-order modeling of*linear**dynamical**systems*, and then give an overview of the recent progress in ... Thanks to Louis Komzsik and Tom Kowalski*for*providing case studies from structural*dynamics*. ...
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