Geometry in the Neighbourhood of Invariant Manifold of Maps and Flows and Linearization

103 Pages·1990·4.637 MB·English

by  U. Kirchgraber, K.J. Palmer

Ji
Pitman Research Notes in Mathematics Series 233
U Kirchgraber & K J Palmer
Geometry in the
neighborhood of
invariant manifolds of
maps and flows and
linearization
Longman
mmm
Scientific &
n u n
Technical
Pitman Research Notes in Mathematics
Series
Main Editors
H. Brezis, Université de Paris
R. G. Douglas, State University of New York at Stony Brook
A. Jeffrey, University of Newcastle-upon-Tyne (Founding Editor)
Editorial Board
R. Aris, University of Minnesota B. Lawson, State University of New York at
A. Bensoussan, INRIA, France Stony Brook
S. Bloch, University of Chicago W. F. Lucas, Claremont Graduate School
B. Bollobâs, University of Cambridge R. E. Meyer, University of Wisconsin-Madison
W. Bürger, Universität Karlsruhe S. Mori, Kyoto University
S. Donaldson, University of Oxford L. E. Payne, Cornell University
J. Douglas Jr, University of Chicago G. F. Roach, University of Strathclyde
R. J. Elliott, University of Alberta J. H. Seinfeld, California Institute of
G. Fichera, Université di Roma Technology
R. P. Gilbert, University of Delaware B. Simon, California Institute of Technology
R. Glowinski, Université de Paris I. N. Stewart, University of Warwick
K. P. Hadeler, Universität Tübingen S. J. Taylor, University of Virginia
K. Kirchgässner, Universität Stuttgart
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Titles in this series
1 Improperly posed boundary value problems 27 Nonlinear analysis and mechanics:
A Carasso and A P Stone Heriot-Watt Symposium Volume II
2 Lie algebras generated by finite dimensional R J Knops
ideals 28 Constructive functional analysis
IN Stewart D S Bridges
3 Bifurcation problems in nonlinear 29 Elongational flows: Aspects of the behaviour
elasticity of model elasticoviscous fluids
R W Dickey C J S Petrie
4 Partial differential equations in the complex 30 Nonlinear analysis and mechanics:
domain Heriot-Watt Symposium Volume III
D L Colton R J Knops
5 Quasilinear hyperbolic systems and waves 31 Fractional calculus and integral transforms of
A Jeffrey generalized functions
6 Solution of boundary value problems by the A C McBride
method of integral operators 32 Complex manifold techniques in theoretical
D L Colton physics
7 Taylor expansions and catastrophes D E Lerner and P D Sommers
T Poston and IN Stewart 33 Hilbert’s third problem: scissors congruence
8 Function theoretic methods in differential C-H Sah
equations 34 Graph theory and combinatorics
R P Gilbert and R J Weinacht RJ Wilson
9 Differential topology with a view to 35 The Tricomi equation with applications to the
applications theory of plane transonic flow
D R J Chillingworth A R Manwell
10 Characteristic classes of foliations 36 Abstract differential equations
H V Pittie S D Zaidman
11 Stochastic integration and generalized 37 Advances in twistor theory
martingales L P Hughston and R S Ward
A U Kussmaul 38 Operator theory and functional analysis
12 Zeta-functions: An introduction to algebraic I Erdelyi
geometry 39 Nonlinear analysis and mechanics:
A D Thomas Heriot-Watt Symposium Volume IV
13 Explicit a priori inequalities with applications to R J Knops
boundary value problems 40 Singular systems of differential equations
V G Sigillito S L Campbell
14 Nonlinear diffusion 41 N-dimensional crystallography
W E Fitzgibbon III and H F Walker RLE Schwarzenberger
15 Unsolved problems concerning lattice points 42 Nonlinear partial differential equations in
J Hammer physical problems
16 Edge-colourings of graphs D Graffi
S Fiorini and R J Wilson 43 Shifts and periodicity for right invertible
17 Nonlinear analysis and mechanics: operators
Heriot-Watt Symposium Volume I D Przeworska-Rolewicz
R J Knops 44 Rings with chain conditions
18 Actions of fine abelian groups A W Chatters and C R Hajarnavis
C Kosniowski 45 Moduli, deformations and classifications
19 Closed graph theorems and webbed spaces of compact complex manifolds
M De Wilde D Sundararaman
20 Singular perturbation techniques applied to 46 Nonlinear problems of analysis in
integro-differential equations geometry and mechanics
H Grabmiiller M Atteia, D Bancel and I Gumowski
21 Retarded functional differential equations: 47 Algorithmic methods in optimal control
A global point of view W A Gruver and E Sachs
SEA Mohammed 48 Abstract Cauchy problems and
22 Multiparameter spectral theory in Hilbert space functional differential equations
B D Sleeman F Kappel and W Schappacher
24 Mathematical modelling techniques 49 Sequence spaces
R Aris W H Ruckle
25 Singular points of smooth mappings 50 Recent contributions to nonlinear
C G Gibson partial differential equations
26 Nonlinear evolution equations solvable by the H Berestycki and H Brezis
spectral transform 51 Subnormal operators
F Calogero J B Conway
52 Wave propagation in viscoelastic media 76 Clifford analysis
F Mainardi F Brackx, R Delanghe and F Sommen
53 Nonlinear partial differential equations and 77 Nonlinear equivalence, reduction of PD Es
their applications: Collège de France to ODEs and fast convergent numerical
Seminar. Volume I methods
H Brezis and J L Lions E E Rosinger
54 Geometry of Coxeter groups 78 Free boundary problems, theory and
H Hiller applications. Volume I
55 Cusps of Gauss mappings A Fasano and M Primicerio
T Banchoff, T Gaffney and C McCrory 79 Free boundary problems, theory and
56 An approach to algebraic K-theory applications. Volume II
A J Berrick A Fasano and M Primicerio
57 Convex analysis and optimization 80 Symplectic geometry
J-P Aubin and R B Vintner A Crumeyrolle and J Grifone
58 Convex analysis with applications in 81 An algorithmic analysis of a communication
the differentiation of convex functions model with retransmission of flawed messages
J R Giles D M Lucantoni
59 Weak and variational methods for moving 82 Geometric games and their applications
boundary problems W H Ruckle
C M Elliott and J R Ockendon 83 Additive groups of rings
60 Nonlinear partial differential equations and S Feigelstock
their applications: Collège de France 84 Nonlinear partial differential equations and
Seminar. Volume II their applications: Collège de France
H Brezis and J L Lions Seminar. Volume IV
61 Singular systems of differential equations II H Brezis and J L Lions
S L Campbell 85 Multiplicative functionals on topological algebras
62 Rates of convergence in the central limit T Husain
theorem 86 Hamilton-Jacobi equations in Hilbert spaces
Peter Hall V Barbu and G Da Prato
63 Solution of differential equations 87 Harmonic maps with symmetry, harmonic
by means of one-parameter groups morphisms and deformations of metrics
J M Hill P Baird
64 Hankel operators on Hilbert space 88 Similarity solutions of nonlinear partial
S C Power differential equations
65 Schrödinger-type operators with continuous L Dresner
spectra 89 Contributions to nonlinear partial differential
MSP Eastham and H Kalf equations
66 Recent applications of generalized inverses C Bardos, A Damlamian, JI Diaz and
S L Campbell J Hernández
67 Riesz and Fredholm theory in Banach algebra 90 Banach and Hilbert spaces of vector-valued
B A Barnes, G J Murphy, M R F Smyth and functions
T T West J Burbea and P Masani
68 Evolution equations and their applications 91 Control and observation of neutral systems
F Kappel and W Schappacher D Salamon
69 Generalized solutions of Hamilton-Jacobi 92 Banach bundles, Banach modules and
equations automorphisms of C*-algebras
P L Lions M J Dupré and R M Gillette
70 Nonlinear partial differential equations and 93 Nonlinear partial differential equations and
their applications: Collège de France their applications: Collège de France
Seminar. Volume III Seminar. Volume V
H Brezis and J L Lions H Brezis and J L Lions
71 Spectral theory and wave operators for the 94 Computer algebra in applied mathematics:
Schrôdinger equation an introduction to MACSYMA
A M Berthier R H Rand
72 Approximation of Hilbert space operators I 95 Advances in nonlinear waves. Volume I
D A Herrero L Debnath
73 Vector valued Nevanlinna Theory 96 FC-groups
HJWZiegler M J Tomkinson
74 Instability, nonexistence and weighted 97 Topics in relaxation and ellipsoidal methods
energy methods in fluid dynamics M Akgiil
and related theories 98 Analogue of the group algebra for
B Straughan topological semigroups
75 Local bifurcation and symmetry H Dzinotyiweyi
A Vanderbauwhede 99 Stochastic functional differential equations
SEA Mohammed
100 optimal control of variational inequalities 125 Ennio de Giorgi Colloquium
V Barbu P Krée
101 Partial differential equations and 126 Almost-periodic functions in abstract spaces
dynamical systems S Zaidman
W E Fitzgibbon III 127 Nonlinear variational problems
102 Approximation of Hilbert space operators. A Marino, L Módica, S Spagnolo and
Volume II M Degiovanni
C Apostol, L A Fialkow, D A Herrero and 128 Second-order systems of partial differential
D Voiculescu equations in the plane
103 Nondiscrete induction and iterative processes L К Hua, W Lin and C-Q Wu
V Ptak and F-A Potra 129 Asymptotics of high-order ordinary differential
104 Analytic functions - growth aspects equations
O P Juneja and G P Kapoor R В Paris and A D Wood
105 Theory of Tikhonov regularization for 130 Stochastic differential equations
Fredholm equations of the first kind R Wu
C W Groetsch 131 Differential geometry
106 Nonlinear partial differential equations L A Cordero
and free boundaries. Volume I 132 Nonlinear differential equations
J I Diaz J К Hale and P Martinez-Amores
107 Tight and taut immersions of manifolds 133 Approximation theory and applications
T E Cecil and P J Ryan S P Singh
108 A layering method for viscous, incompressible 134 Near-rings and their links with groups
Lp flows occupying R" J D P Meldrum
A Douglis and E B Fabes 135 Estimating eigenvalues with a posteriorUa priori
109 Nonlinear partial differential equations and inequalities
their applications: Collège de France J R Kuttler and V G Sigillito
Seminar. Volume VI 136 Regular semigroups as extensions
H Brezis and J L Lions F J Pastijn and M Petrich
110 Finite generalized quadrangles 137 Representations of rank one Lie groups
S E Payne and J A Thas D H Collingwood
111 Advances in nonlinear waves. Volume II 138 Fractional calculus
L Debnath G F Roach and A C McBride
112 Topics in several complex variables 139 Hamilton’s principle in
E Ramirez de Arellano and D Sundararaman continuum mechanics
113 Differential equations, flow invariance A Bedford
and applications 140 Numerical analysis
N H Pavel D F Griffiths and G A Watson
114 Geometrical combinatorics 141 Semigroups, theory and applications. Volume I
F C Holroyd and R J Wilson H Brezis, M G Crandall and F Kappel
115 Generators of strongly continuous semigroups 142 Distribution theorems of L-functions
J A van Casteren D Joyner
116 Growth of algebras and Gelfand-Kirillov 143 Recent developments in structured continua
dimension D De Кее and P Kaloni
G R Krause and T H Lenagan 144 Functional analysis and two-point differential
117 Theory of bases and cones operators
P K Kamthan and M Gupta J Locker
118 Linear groups and permutations 145 Numerical methods for partial differential
A R Camina and E A Whelan equations
119 General Wiener-Hopf factorization methods S I Hariharan and T H Moulden
F-0 Speck 146 Completely bounded maps and dilations
120 Free boundary problems: applications and V I Paulsen
theory. Volume III 147 Harmonic analysis on the Heisenberg nilpotent
A Bossavit, A Damlamian and M Fremond Lie group
121 Free boundary problems: applications and W Schempp
theory, Volume IV 148 Contributions to modern calculus of variations
A Bossavit, A Damlamian and M Fremond L Cesari
122 Nonlinear partial differential equations and 149 Nonlinear parabolic equations: qualitative
their applications: Collège de France properties of solutions
Seminar. Volume VII L Boccardo and A Tesei
H Brezis and J L Lions 150 From local times to global geometry, control and
123 Geometric methods in operator algebras physics
H Araki and E G Effros К D Ehvorthy
124 Infinite dimensional analysis-stochastic
processes
S Albeverio
151 A stochastic maximum principle for optimal 177 Cordes’ two-parameter spectral representation
control of diffusions theory
U G Haussmann D F McGhee and R H Picard
152 Semigroups, theory and applications. Volume II 178 Equivariant K-theory for
H Brezis, M G Crandall and F Kappel proper actions
153 A general theory of integration in function N C Phillips
spaces 179 Elliptic operators, topology
P Muldowney and asymptotic methods
154 Oakland Conference on partial differential J Roe
equations and applied mathematics 180 Nonlinear evolution equations
L R Bragg and J W Dettman J K Engelbrecht, V E Fridman and
155 Contributions to nonlinear partial differential E N Pelinovski
equations. Volume II 181 Nonlinear partial differential equations and their
JI Diaz and P L Lions applications. Collège de France Seminar. Volume
156 Semigroups of linear operators: an introduction IX
A C McBride H Brezis and J L Lions
157 Ordinary and partial differential equations 182 Critical points at infinity in some variational
B D Sleeman and R J Jarvis problems
158 Hyperbolic equations A Bahri
F Colombini and M K V Murthy 183 Recent developments in hyperbolic equations
159 Linear topologies on a ring: an overview L Cattabriga, F Colombini, M K V Murthy and S
J S Golan Spagnolo
160 Dynamical systems and bifurcation theory 184 Optimization and identification of systems
MI Camacho, M J Pacifico and F Takens governed by evolution equations on Banach space
161 Branched coverings and algebraic functions N U Ahmed
M Namba 185 Free boundary problems: theory and applications.
162 Perturbation bounds for matrix eigenvalues Volume I
R Bhatia K H Hoffmann and J Sprekels
163 Defect minimization in operator equations: 186 Free boundary problems: theory and applications.
theory and applications Volume II
R Reemtsen K H Hoffmann and J Sprekels
164 Multidimensional Brownian excursions and 187 An introduction to intersection homology theory
potential theory F Kirwan
K Burdzy 188 Derivatives, nuclei and dimensions on the frame
165 Viscosity solutions and optimal control of torsion theories
R J Elliott J S Golan and H Simmons
166 Nonlinear partial differential equations and 189 Theory of reproducing kernels and its applications
their applications. Collège de France Seminar. S Saitoh
Volume VIII 190 Volterra integrodifferential equations in Banach
H Brezis and J L Lions spaces and applications
167 Theory and applications of inverse problems G Da Prato and M lannelli
H Haario 191 Nest algebras
168 Energy stability and convection K R Davidson
G P Galdi and B Straughan 192 Surveys of some recent results in operator theory.
169 Additive groups of rings. Volume II Volume II
S Feigelstock J B Conway and B B Morrel
170 Numerical analysis 1987 193 Nonlinear variational problems. Volume II
D F Griffiths and G A Watson A Marino and M K Murthy
171 Surveys of some recent results in 194 Stochastic processes with multidimensional
operator theory. Volume I parameter
J B Conway and B B Morrel M E Dozzi
172 Amenable Banach algebras 195 Prestressed bodies
J.P Pier D lesan
173 Pseudo-orbits of contact forms 196 Hilbert space approach to some classical
A Bahri transforms
174 Poisson algebras and Poisson manifolds R H Picard
K H Bhaskara and K Viswanath 197 Stochastic calculus in application
175 Maximum principles and J R Norris
eigenvalue problems in 198 Radical theory
partial differential equations B J Gardner
P W Schaefer 199 The C* - algebras of a class of solvable Lie
176 Mathematical analysis of groups
nonlinear, dynamic processes XWang
K U Grusa
200 Stochastic analysis, path integration and 225 Surveys of some recent results in operator theory.
dynamics Volume III
D Elworthy J В Conway and В В Morrel
201 Riemannian geometry and holonomy groups 226 Local cohomology and localization
S Salamon J L Bueso Montero, В Torrecillas Jover and
202 Strong asymptotics for extremal errors and A Verschoren
polynomials associated with Erdos type weights 227 Sobolev spaces of holomorphic functions
D S Lubinsky F Beatrous and J Burbea
203 Optimal control of diffusion processes 228 Numerical analysis. Volume III
V S Borkar D F Griffiths and G A Watson
204 Rings, modules and radicals 229 Recent developments in structured continua.
B J Gardner Volume III
205 Numerical studies for nonlinear Schrödinger D De Kee and P Kaloni
equations 230 Boolean methods in interpolation and
B M Herbst and J A C Weideman approximation
206 Distributions and analytic functions F J Delvos and W Schempp
R D Carmichael and D Mitrovic 231 Further advances in twistor theory. Volume 1
207 Semicontinuity, relaxation and integral L J Mason and L P Hughston
representation in the calculus of variations 232 Further advances in twistor theory. Volume 2
G Buttazzo L J Mason and L P Hughston
208 Recent advances in nonlinear elliptic and 233 Geometry in the neighborhood of invariant
parabolic problems manifolds of maps and flows and linearization
P B^nilan, M Chipot, L Evans and M Pierre U Kirchgraber and К Palmer
209 Model completions, ring representations and the 234 Quantales and their applications
topology of the Pierce sheaf КI Rosenthal
A Carson
210 Retarded dynamical systems
G Stepan
211 Function spaces, differential operators and
nonlinear analysis
L Paivarinta
212 Analytic function theory of one complex
variable
C C Yang, Y Komatu and K Niino
213 Elements of stability of visco-elastic fluids
J Dunwoody
214 Jordan decompositions of generalised vector
measures
K D Schmidt
215 A mathematical analysis of bending of plates
with transverse shear deformation
C Constanda
216 Ordinary and partial differential equations
Vol II
B D Sleeman and R J Jarvis
217 Hilbert modules over function algebras
R G Douglas and VI Paulsen
218 Graph colourings
R Wilson and R Nelson
219 Hardy-type inequalities
A Kufner and B Opic
220 Nonlinear partial differential equations and
their applications. College de France Seminar
Volume X
H Brezis and J L Lions
221 Workshop on dynamical systems
E Shiels and Z Coelho
222 Geometry and analysis in nonlinear dynamics
H W Broer and F Takens
223 Fluid dynamical aspects of combustion theory
M Onofri and A Tesei
224 Approximation of Hilbert space operators.
Volume I. 2nd edition
D Herrero
Geometry in the
neighborhood of
invariant manifolds of
maps and flows and
linearization

U Kirchgraber
Swiss Federal Institute of Technology
&
K J Palmer
University of Miami
Geometry in the
neighborhood of
invariant manifolds of
maps and flows and
linearization
Longman
Scientific 8c
Technical
Copublished in the United States with
John Wiley 8i Sons, Inc., New York