Estimates of the periods of periodic points for nonexpansive operators

M. A. Akcoglu and U. Krengel,Nonlinear models of diffusion on a finite space, Probab. Theor. Relat. Fields76 (1987), 411–420.

A. Blokhuis and H. A. Wilbrink,Alternative proof of Nussbaum’s theorem on the size of a regular polygon in ℝ n with the ℓ∞-metric, preprint.

W. Chou and R. J. Duffin,An additive eigenvalue problem of physics related to linear programming, Advances in Appl. Math.8 (1987), 486–498.

W. Chou and R. B. Griffiths,Ground states of one dimensional systems using effective potentials, Phys. Rev. B34 (1986), 6219–6234.

M. G. Crandall and L. Tartar,Some relations between nonexpansive and order preserving mappings, Proc. Am. Math. Soc.78 (1980), 385–391.

R. A. Cuninghame-Green,Minimax Algebra, Springer Lecture Notes in Economics and Mathematical Systems, Vol. 166, Springer-Verlag, Berlin, 1979.

L. M. Floria and R. B. Griffiths,Numerical procedure for solving a minimization eigenvalue problem, Numerische Math.55 (1989), 565–574.

R. B. Griffiths, personal letter to R. D. Nussbaum, May, 1990.

R. M. Karp,A characterization of the minimum cycle mean in a digraph, Discrete Math.23 (1978), 309–311.

R. D. Nussbaum,Hilbert’s projective metric and iterated nonlinear maps, Memoirs Am. Math. Soc. No. 391 (1988).

R. D. Nussbaum,Hilbert’s projective metric and interated nonlinear maps, II, Memoirs Am. Math. Soc. No. 401 (1989).

R. D. Nussbaum,Omega limit sets of nonexpansive maps: finiteness and cardinality estimates, Diff. and Integral Equations3 (1990), 523–540.

R. D. Nussbaum,Convergence of iterates of a nonlinear operator arising in statistical mechanics, Nonlinearity4 (1991), 1223–1240.

J. B. Rosser and L. Schoenfeld,Approximate formulas for some functions of prime numbers, Illinois J. Math.6 (1962), 64–94.

M. Scheutzow,Periods of nonexpansive operators on finite ℓ 1-spaces, European J. Combinatorics9 (1988), 73–81.

M. Scheutzow,Correction to periods of nonexpansive operators on finite ℓ 1-spaces, to appear.

E. Seneta,Nonnegative Matrices: An Introduction to Theory and Applications, George Allen and Unwin, London, 1973.

R. Sine,A nonlinear Perron-Frobenius theorem, Proc. Am. Math. Soc.109 (1990), 331–336.

D. Weller,Hilbert’s metric, part metric and self mappings of a cone, Ph.D. dissertation, Univ. of Bremen, West Germany, December 1987.