Roger D. Nussbaum

Professor of Mathematics
Rutgers, The State University Of New Jersey
110 Frelinghuysen Road
Piscataway, NJ 08854-8019

Phone: (732) 445-3070
Fax: (732) 445-5530

Publications Available Online
Title Journal Date

The fixed point index for local condensing maps

Annali di Matematici, 89 (1971), 217-258 1971
Cyclic differential equations and period three solutions of differential-delay equations Journal of Differential Equations, 48 (1982), 379-408 1982
The fixed point index and some applications Séminaire de Mathématiques Supérieures, Université de Montréal 1985
Circulant matrices and differential-delay equations Journal of Differential Equations, 60 (1985), 201-217 1985
Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation Annali Matematica Pura ed Applicata, 145 (1986), 33-128 1986
Convexity and log convexity for the spectral radius Linear Algebra and its Applications, 73 (1986), 59-122 1986
A differential-delay equation arising in optics and physiology SIAM Journal of Mathematical Aanlysis, 20 (1989), 249-292 1989
The arithmetic-geometric mean and its generalizations for noncommuting linear operators Annali Scuola Normale di Pisa, 15 (1989), 239-308 1989
Some nonlinear weak ergodic theorems SIAM Journal of Mathematical Analysis, 21 (1990), 436-460 1990
Estimates of the periods of periodic points for nonexpansive operators Israel Journal of Mathematics, 76 (1991), 345-380 1991
Convergence of iterates of a nonlinear operator arising in statistical mechanics Nonlinearity 4 (1991), 1223-1240 1991
Boundary layer phenomena for differential-delay equations with state-dependent time lags, I Archive for Rational Mechanics and Analysis, 120 (1992), 99-146 1992
On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications Journal d'Analyse Mathematique, 59 (1992), 161-177 1992
Entropy Minimization, Hilbert’s Projective Metric, and Scaling Integral Kernels Journal of Functional Analysis 115, 45-99 1993
A limit set trichotomy for self-mappings of normal cones in Banach spaces Nonlinear Analysis, T.M.and A., 20 (1993), 855-870 1993
Periodic Solutions for Functional Differential Equations with Multiple State-dependent Time Lags Topological Methods in Nonlinear Analysis 3(1994), pp. 101-162 1994
Lattice Isomorphisms and Iterates of Nonexpansive Maps Nonhnear Analysis, Theory, Methods & Applications, 22 (8), pp. 945-970 1994
Entropy minimization, DAD theorems and doubly stochastic kernels Journal of Functional Analysis, 123 (1994), 264-307 1994

Finsler structures for the part metric and Hilbert’s projective metric and applicationsto ordinary differential equations

Differential and Integral Equations, 7 (1994), 1649-1707.

1994
Applications of the Birkhoff-Hopf theorem to the spectral theory of positive linear operators Proceedings of the Cambridge Philosophical Society, 117 (1995), 491-512 1995
An elementary proof of the Birkhoff-Hopf theorem Mathematical Proceedings of the Cambrdige Philosophical Society, 117 (1995), 31-55 1995
Boundary Layer Phenomena for Differential-delay Equations with State Dependent Time Lags: II Journal für die Reine und Angewandte Mathematik 477 (1996), pp. 129-197 1996
Eigenvectors of order-preserving linear operators Journal of London Mathematical Society, 58 (1998), 480-496 1998
Approximation by Polynomials with Nonnegative Coefficients and the Spectral Theory of Positive Operators Transactions of the American Mathematical Society 350 (6), 2367-2391 1998
Periodic points of nonexpansive maps and nonlinear genralizations of the Perron-Frobenius theory Selecta Mathematica 4 (1998), 141-181 1998
Admissible arrays and a nonlinear generalization of Perron-Frobenius theory Journal of the London Mathematical Society, 58 (1998), 526-544 1998
Dynamics of a Quadratic Map in Two Complex Variables Journal of Differential Equations 169, pp. 57-141 2001
Lower and Upper Bounds for ω-limit sets of Nonexpansive Maps Indag. Mathem., N.S. 12 (2), 191-211 2001
Nonexpansive Periodic Operators in l1 with Application to Superhigh-Frequency Oscillations in a Discontinuous Dynamical System with Time Delay Journal of Dynamics and Differential Equations 13 (2) 2001
Periodic Points of Positive Linear Operators and Perron-Frobenius Operators Integr. Equ. Oper. Theory 39 (2001) 41-97 2001
Eigenvalues For A Class Of Homogeneous Cone Maps Arising From Max-Plus Operators Discrete And Continuous Dynamical Systems, 8 (3) July 2002, 519-562 2002
Existence, Uniqueness and Analyticity for Periodic Solutions of a Non-Linear Convolution Equation Integr. Equ. Oper. Theory 42 (2002) pp. 385-424 2002
A Basis Theorem for a Class of Max-plus Eigenproblems J. Differential Equations 189 (2003), pp. 616–639 2003
Asymptotic estimates for the periods of periodic points of non-expansive maps Ergodic Theory and Dynamical Systems, 23 (2003), 1199-1226 2003
Boundary layer phenomena for differential-delay equations with state-dependent time lags: III Journal of Differential Equations 189 (2003), 640-692 2003
Extension of order-preserving maps on a cone Proceedings of the Royal Society of Edinburgh, 133 (2003), 35-59 2003
Iteration of order preserving subhomogeneous maps on a cone Mathematical Proceedings of the Cambridge Philosophical Society, 140 (2006), 157-176 2006
Iterated linear maps on a cone and Denjoy-wolff theorems Linear algebra and its Applications, 416 (2006), pages 615-626 2006
Global Stablility, Two Conjectures, and Maple Nonlinear Analysis, Vol.66, (5), pp. 1064-1090 2007
Fixed Point Theorems, and Denjoy-Wolff Theorems for Hilbert's Projective Metric in Infinite Dimensions Topological Methods in Nonlinear Analysis, 29 (2007) pp.199-249 2007
Asymptotic Fixed Point Theory and the Beer Barrel Theorem J. Fixed Point Theory and Applications 4 (2008), 203-245 2008
Denjoy–Wolff theorems, Hilbert metric nonexpansive maps and reproduction–decimation operators J. Functional Analysis 254 (2008), 2365-2386 2008
Generalizing the Krein-Rutman Theorem, Measures of Noncompactness and the Fixed Point Index J. Fixed Point Theory and Applications 7 (2010), 103-143 2010
Inequivalent Measures of Noncompactness Annali di Matematica Pura ed Applicata, 190, Issue 3 (2011), 453-488 2011
Superstability and Rigorous Asymptotics in Singularly Perturbed State-Dependent Delay-Differential Equations Journal of Differential Equations 250 (2011), 4037-4084 2011
Stability of Periodic Solutions of State-Dependent Delay-Differential Equations Journal of Differential Equations 250 (2011), 4085-4103 2011
Inequivalent Measures of Noncompactness and the Radius of the Essential Spectrum Proceedings of American Math. Society 139 (2011), 917-930 2011
Positive Operators and Hausdorff Dimension of Invariant sets Transactions of American Math Society, 364 (2012), 1029-1066 2012
Tensor Products, Positive Linear Operators, and Delay-Differential Equations. Available at http://arXiv.org/abs/1210.0919v1. Journal of Dynamics and Differential Equations 25 (2013), 843-905 2012
Continuity of the Cone Spectral Radius Proceedings of American Math. Society 141 (2013), 2741-2754 2013
Analyticity and non-analyticity of solutions of delay-differential equations (John Mallet-Paret and Roger Nussbaum) [available at arXiv:1305.0579] SIAM Journal of Mathematical Analysis 46 (2014), 2468-2500 2014
Uniqueness of the fixed point of nonexpansive semi-differentiable maps (Marianne Akian, Stephane Gaubert and Roger Nussbaum) Transactions of the American Math. Society,368 (2016), 1271-1320 (published electronically 2/19/15) 2015
Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces (Bas Lemmens, Brian Lins, Roger D. Nussbaum, and Marten Wortel), Available at http://arXiv.org/abs/1410.1056.

accepted for publication in J. d'Analyse Mathematique

 
Birkhoff's version of Hilbert's metric and its applications in analysis (Bas Lemmens and Roger D. Nussbaum). Available at http://arXiv.org/abs/1304.7921. Handbook of Hilbert Geometry, edited by G. Besson, A. Papadopoulos, and M. Troyanov, Chapter 10 2014
A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones (Marianne Akian, Stephan Gaubert, and Roger D. Nussbaum). Available at http://arXiv.org/abs/1112.5968v2. submitted for publication  
Positive Eigenvectors for Linear Operators Arising in the Computation of Hausdorff Dimension Integral Equations and Operator Theory 84 (2016), 357-393 2016
Cm Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Applications in R1 (Roger D. Nussbaum and Richard S. Falk) submitted for publication; available at http://arXiv.org/abs/1612.00870  
Cm Eigenfunctions of Perron-Frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Complex Continued Fractions (Roger D. Nussbaum and Richard S. Falk) submitted for publication; available at http://arXiv.org/abs/1612.00869  
Gevrey Class Regularity for Analytic Differential-Delay Equations (Roger D. Nussbaum and Gabriella Vas) accepted for publication in Electronic Journal of the Qualitative Theory of Differential Equations  
Detecting fixed points of nonexpansive maps by illuminating the unit ball (Bas Lemmens, Brian Lins, and Roger D. Nussbaum) submitted for publicication; available at http://arXiv.org/abs/1607.01602  

Last modified 6/11/18