Selected research publications by George R Sell are cited below. An abstract, if available, can be obtained by clicking on abstract. Happy Reading!!

Home Page of George R Sell

Also see
**
4. Control Theory,
7. Exponential Dichotomies and Exponential Trichotomies,
9. Linear Dynamical Systems,
and
11. Skew Product Flows: Nonautonomous Dynamics.
**

4.
L G Deysach and G R Sell (1965),
On the existence of almost periodic motions.
** Michigan Math J,**
Vol 12, pages 87-95.

50.
G R Sell (1975),
** Linear Differential Systems **,
Lecture Notes, University of Minnesota, 1975.

59.
R J Sacker and G R Sell (1977),
** Lifting Properties in Skew Product Flows with Applications
to Differential Equations **,
Memoir Amer Math Soc, No 190, 1977.

61.
G R Sell (1977),
Hyperbolic almost periodic solutions and toroidal limit sets.
** Proc Nat Acad Sci, USA,**
Vol 74, pages 3124-3125.

74.
G R Sell (1981),
A remark on an example of R A Johnson.
** Proc Amer Math Soc,**
Vol 82, pages 206-208.

99.
K R Meyer and G R Sell (1989),
Melnikov transformations, Bernoulli bundles and almost periodic perturbations.
** Trans Amer Math Soc,**
Vol 314, pages 63-105.

129.
G R Sell and Y You (2002),
** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

104.
V A Pliss and G R Sell (1991),
Perturbation of attractors of differential equations,
**
J. Differential Equations,
**
Vol 92, pages 100-124.

124.
V A Pliss and G R Sell (1998),
Approximation dynamics and the stability of invariant sets,
** J Differential Equations,**
Vol 149, pages 1-51.
abstract,

125.
V A Pliss and G R Sell (1999),
Robustness of exponential dichotomies in infinite dimensional systems,
** J Dynamics Differential Equations,**
Vol 11, pages 471-513.

127.
V A Pliss and G R Sell (2001),
Perturbations of normally hyperbolic manifolds with applications to the
Navier-Stokes equations,
** J Differential Equations,**
Vol 169, pages 396-492.

V A Pliss and G R Sell (2001 exp)
Stability of normally hyperbolic sets of smooth flows.
** Doklady Akademii Nauk,**
(to appear)

129.
G R Sell and Y You (2002),
** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

66.
G R Sell (1979),
Bifurcation of higher dimensional tori.
** Arch Rational Mech Anal,**
Vol 69, pages 199-230.

79.
G R Sell (1981),
Hopf-Landau bifurcation near strange attractors.
in
** Chaos and Order in Nature,**
pages 84-91, Springer.

82.
G R Sell (1983),
Resonance and bifurcations in Hopf-Landau dynamical systems.
in
** Turbulence and Nonlinear Dynamics,**
pages 305-313, Pitman.

99.
K R Meyer and G R Sell (1989),
Melnikov transformations, Bernoulli bundles and almost periodic perturbations.
** Trans Amer Math Soc,**
Vol 314, pages 63-105.

21.
L Markus and G R Sell (1968),
Capture and control in conservative dynamical systems.
** Arch Rational Mech Anal,**
Vol 31, pages 271-287.

48.
L Markus and G R Sell (1974),
Control in conservative dynamical systems.
Recurrence and capture in aperiodic fields.
** J Differential Equations,**
Vol 16, pages 472-505.

118.
J Mallet-Paret and G R Sell (1996),
Systems of delay differential equations I:
Floquet multipliers and discrete Lyapunov functions.
** J Differential Equations,**
Vol 125, pages 385-440.

119.
J Mallet-Paret and G R Sell (1996),
The Poincare-Bendixson theorem for monotone cyclic feedback systems
with delay.
** J Differential Equations,**
Vol 125, pages 441-489.
abstract.

Inertial Manifolds and Finite Dimensional Structures

93.
C Foias, G R Sell, and R Temam (1988),
Inertial manifolds for nonlinear evolutionary equations.
** J Differential Equations,**
Vol 73, pages 309-353.

94.
C Foias, B Nicolaenko, G R Sell, and R Temam (1988),
Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of
their lowest dimension.
** J Math Pures Appl,**
Vol 67, pages 197-226.

95.
C Foias, M S Jolly, I G Kevrekidis, G R Sell, and E S Titi (1988),
On the computation of inertial manifolds.
** Physics Letters A,**
Vol 131, pages 433-436.

96.
J Mallet-Paret and G R Sell (1988),
Inertial manifolds for reaction diffusion equations in higher space dimensions.
** J Amer Math Soc,**
Vol 1, pages 805-866.

97.
C Foias, G R Sell, and E S Titi (1989),
Exponential tracking and approximation of inertial manifolds.
** J Dynamics Differential Equations,**
Vol 1, pages 199-244.

100.
G R Sell (1989),
Hausdorff and Lyapunov dimensions for gradient systems.
** Contemporary Math Series,**
Vol 99, pages 85-92.

103.
E Fabes, M Luskin, and G R Sell (1991),
Construction of inertial manifolds by elliptic regularization.
** J Differential Equations,**
Vol 89, pages 355-387.

106.
G R Sell and Y You (1992),
Inertial manifolds: The non-self adjoint case.
** J Differential Equations,**
Vol 96, pages 203-255.

107.
G R Sell and M Taboada (1992),
Local dissipativity and attractors for the Kuramoto-Sivashinsky
equation in thin 2D domains.
** Nonlinear Anal, TMA,**
Vol 18, pages 671-687.

108.
S-N Chow, K Lu, and G R Sell (1992),
Smoothness of inertial manifolds.
** J Math Anal Appl,**
Vol 169, pages 283-312.

112.
G R Sell (1993),
An optimality condition for approximate inertial manifolds.
in
** Turbulence in Fluid Flows: A Dynamical Systems Approach**,
IMA Volumes in Mathematics and its Applications, vol 55, 1993,
pages 165-186,
Springer Verlag.

114.
J Mallet-Paret, G R Sell, and Z Shao (1993),
Obstructions for the existence of normally hyperbolic inertial manifolds.
** Indiana J Math,**
Vol 42, pages 1027-1055.

126.
A V Babin and G R Sell (2000),
Attractors of nonautonomous parabolic equations and their symmetry
properties.
** J Differential Equations,**
Vol 160, pages 1-50.

129.
G R Sell and Y You (2002),
** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

45.
R J Sacker and G R Sell (1974),
Existence of dichotomies and invariant splittings for linear differential
systems I,
** J Differential Equations**,
Vol 15, pages 429-458.

57.
R J Sacker and G R Sell (1976),
Existence of dichotomies and invariant splittings for linear differential
systems II,
** J Differential Equations**,
Vol 22, pages 478-496.

58.
R J Sacker and G R Sell (1976),
Existence of dichotomies and invariant splittings for linear differential
systems III,
** J Differential Equations**,
Vol 22, pages 497-522.

116.
R J Sacker and G R Sell (1994),
Dichotomies in linear evolutionary equations in Banach spaces,
** J Differential Equations**,
Vol 113, pages 17-67.

125.
V A Pliss and G R Sell (1999),
Robustness of exponential dichotomies in infinite dimensional systems,
** J Dynamics Differential Equations,**
Vol 11, pages 471-513.

** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

20.
R K Miller and G R Sell (1967),
Existence, uniqueness and continuity of solutions of integral equations.
** Ann Mat Pura Appl,**
Vol 80, pages 135-152.

27.
R K Miller and G R Sell (1970),
** Volterra Integral Equations and Topological Dynamics**,
Memoir Amer Math Soc, No 102, 1970.

39.
G R Sell (1973),
A Tauberian condition and skew product flows with applications to
integral equations.
** J Math Anal Appl,**
Vol 43, pages 388-396.

Also see
** 7. Exponential Dichotomies and Exponential Trichotomies. **

50.
G R Sell (1975),
** Linear Differential Systems, **
Lecture Notes, University of Minnesota, 1975.

64.
R J Sacker and G R Sell (1978),
A spectral theory for linear differential systems.
** J Differential Equations,**
Vol 27, pages 320-358.

71.
R J Sacker and G R Sell (1980),
Singular perturbations and conditional stability.
** J Math Anal Appl,**
Vol 76, pages 406-431.

73.
R J Sacker and G R Sell (1980),
The spectrum of an invariant manifold.
** J Differential Equations,**
Vol 38, pages 135-160.

78.
R A Johnson and G R Sell (1981),
Smoothness of spectral subbundles and reducibility of quasi periodic
linear differential systems.
** J Differential Equations,**
Vol 41, pages 262-288.

83.
G R Sell (1984),
Obstacles to linearization (Russian).
** Differencial'nye Uravnenija,**
Vol 20, pages 446-450.
English translation in
** Differential Equations,**
Vol 20, pages 341-345.

84.
G R Sell (1984),
Linearization and global dynamics.
** Proceedings of the International Congress of Mathematicians,**
Vol 2, pages 1283-1296,
Polish Scientific Publishers, Warsaw.

85.
G R Sell (1985),
Smooth linearization near a fixed point.
** Amer J Math,**
Vol 107, pages 1035-1091.

88.
R A Johnson, K J Palmer, and G R Sell (1987),
Ergodic properties of linear dynamical systems.
** SIAM J Math Anal,**
Vol 18, pages 1-33.

129.
G R Sell and Y You (2002),
** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York

109.
G Raugel and G R Sell (1993),
Navier-Stokes equations on thin 3D domains I:
Global attractors and global regularity of solutions.
** J Amer Math Soc,**
Vol 6, pages 503-568.

110.
G Raugel and G R Sell (1994),
Navier-Stokes equations on thin 3D domains II:
Global regularity of spatially periodic solutions.
in
** Nonlinear Partial Differential Equations and their
Applications, College de France Seminar,**
Vol XI, pages 205-247,
Pitman Research Notes Math, Series 299,
Longman.

111.
G Raugel and G R Sell (1993),
Navier-Stokes equations on thin 3D domains III:
Global and local attractors.
in
** Turbulence in Fluid Flows: A Dynamical Systems Approach**,
IMA Volumes in Mathematics and its Applications, vol 55, 1993,
pages 137-163,
Springer Verlag.

113.
G R Sell, C Foias, and R Temam (editors) (1993),
** Turbulence in Fluid Flows: A Dynamical Systems Approach**,
IMA Volumes in Mathematics and its Applications, vol 55, 1993,
Springer Verlag.

120.
G R Sell (1996),
Global attractors for the three dimensional Navier-Stokes equations,
**
J. Dynamics and Differential Equations,
**
Vol 8, pages 1-33.
abstract,

127.
V A Pliss and G R Sell (2001),
Perturbations of normally hyperbolic manifolds with applications to the
Navier-Stokes equations,
** J Differential Equations,**
Vol 169, pages 396-492.

** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

Also see
** 7. Exponential Dichotomies and Exponential Trichotomies. **

6.
G R Sell (1966),
Periodic solutions and asymptotic stability.
** J Differential Equations,**
Vol 2, pages 143-157.

11.
G R Sell (1967),
Nonautonomous differential equations and topological dynamics I:
The basic theory.
** Trans Amer Math Soc,**
Vol 127, pages 241-262.

12.
G R Sell (1967),
Nonautonomous differential equations and topological dynamics II:
Limiting equations.
** Trans Amer Math Soc,**
Vol 127, pages 263-283.

17.
G R Sell (1968),
Invariant measures and Poisson stability.
** Topological Dynamics,**
pages 435-454,
Benjamin, New York.

29.
G R Sell (1971),
** Topological Dynamics and Differential Equations**,
Lecture Notes, Van Nostrand-Reinhold, 1971.

46.
R J Sacker and G R Sell (1974),
Finite extensions of minimal transformation groups.
** Trans Amer Math Soc,**
Vol 190, pages 325-334.

59.
R J Sacker and G R Sell (1977),
** Lifting Properties in Skew Product Flows with Applications
to Differential Equations **,
Memoir Amer Math Soc, No 190, 1977.

65.
G R Sell (1978),
The structure of a flow in the vicinity of an almost periodic motion.
** J Differential Equations,**
Vol 27, pages 359-393.

70.
G R Sell and F Nakajima (1980),
Almost periodic gross substitute dynamical systems.
** Tohoku Math J,**
Vol 32, pages 255-263.

123.
G R Sell, W Shen, and Y F Yi (1998),
Topological dynamics and differential equations.
in
** Topological Dynamics and Applications;
Contemporary Math Series,**
Vol 215, pages 279-297.

126.
A V Babin and G R Sell (2000),
Attractors of nonautonomous parabolic equations and their symmetry
properties.
** J Differential Equations,**
Vol 160, pages 1-50.

** Dynamics of Evolutionary Equations,**
Vol 143, Applied Mathematical Sciences,
Springer Verlag, New York.

5.
G R Sell (1965),
On the fundamental theory of ordinary differential equations.
** J Differential Equations,**
Vol 1, pages 370-392.

19.
L E Baum and G R Sell (1968),
Growth transformations for functions on manifolds.
** Pacific Math J,**
Vol 27, pages 211-227.

31.
R J Sacker and G R Sell (1972),
On the existence of periodic solutions on 2-manifolds.
** J Differential Equations,**
Vol 11, pages 449-463.

33.
G R Sell (1972),
A characterization of smooth $\alpha$-Lipschitz mappings on a Hilbert space.
** Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur,**
Vol 52, pages 410-416.

38.
G R Sell (1973),
Differential equations without uniqueness and classical topological dynamics.
** J Differential Equations,**
Vol 14, pages 42-56.

52.
G R Sell (1975),
Generic theories in the qualitative theory of ordinary differential equations.
** Boll Un Mat Ital,**
Vol 11, pages 182-188.

122.
A Varghese and G R Sell (1997),
A conservation principle and its effect on the formulation of the
Na-Ca exchanger current in cardiac cells.
** J Theoretical Biology,**
Vol 189, pages 33-40.

Professor George R. Sell

School of Mathematics

University of Minnesota

206 Church Street SE

Minneapolis MN 55455

USA

Phone: 612-625-8381

Fax: 612-626-2017

email: `sell@math.umn.edu
http://www.math.umn.edu/~sell
`

`
`

Date last modified: 26 June 2001.