# Selected Research Publications

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

## 1. Almost Periodicity: Dynamical Theory

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.

## 2. Approximation Dynamics

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.

## 3. Bifurcation Theory

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.

## 4. Control Theory

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.

## 5. Differential-Delay Equations

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.

## 6. Evolutionary Equations: 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.

## 7. Exponential Dichotomies and Exponential Trichotomies

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.

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

## 8. Integral Equations

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.

## 9. Linear Dynamical Systems

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

## 10. Navier-Stokes Equations: Dynamical Issues

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.

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

## 11. Skew Product Flows: Nonautonomous Dynamics

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.

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

## 12. Various Other Areas

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