Periodic points of nonexpansive maps and nonlinear generalizations of the Perron-Frobenius theory

Selecta Mathematica, New Series

Volumn 4, Issue 1, 1998, Pages 141-181

  Nussbaum, Roger D ^a   Scheutzow, Michael ^c   Verduyn Lunel, Sjoerd M ^b  

^a RUTGERS UNIVERSITY   (United States)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Nonexpansive maps; Periods of periodic points of maps; Perron Frobenius theory

Indexed keywords

EID: 54649083065     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050028     Document Type: Article

References (20)

1. M.A. Akcoglu and U. Krengel. Nonlinear models of diffusion on a finite space. Prob. Th. Rel. Fields 76 (1987), 411-420.
2. n with l∞-metric. Discrete Comput. Geometry 7 (1992), 433-434.
3. M.G. Crandall and L. Tartar. Some relations between nonexpansive and order preserving mappings. Proc. Amer. Math. Soc. 78 (1980), 385-391
4. 1. Israel J. Mathematics 58 (1987), 170-192.
5. R. Lyons and R.D. Nussbaum. On transitive and commutative finite groups of isometrics. Fixed Point Theory and Applications (K.-K. Tan, ed.). World Scientific, Singapore, 1992 pp. 189-228.
6. P. Martus. Asymptotic properties of nonstationary operator sequences in the nonlinear case. Ph.D. dissertation, Friedrich-Alexander Univ, Erlangen-Nürnberg (1989).
7. H. Minc. Nonnegative Matrices. John Wiley and Sons, New York, 1988.
8. 1-spaces. Gottingen Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis, Heft 45, 1987.
9. R.D. Nussbaum. Omega limit sets of nonexpansive maps: finiteness and cardinality estimates. Diff. Integral Equations 3 (1990), 523-540.
10. R.D. Nussbaum. Estimates of the periods of periodic points of nonexpansive operators. Israel J. Math. 76 (1991), 345-380.
11. R.D. Nussbaum. Lattice isomorphisms and iterates of nonexpansive maps. Nonlinear Analysis, T.M.A. 22 (1994), 945-970.
12. R.D. Nussbaum. Convergence of iterates of a nonlinear operator arising in statistical mechanics. Nonlinearity 4 (1991), 1223-1240.
13. R.D. Nussbaum. Periodic points of nonexpansive maps. Optimization and Nonlinear Analysis (A. loffe, M. Markus and S. Reich, ed.). Pitman Research Notes in Math. Series, vol. 244, Longman Scientific and Technical, Harlow, UK, 1992, pp. 214-226.
14. R.D. Nussbaum. A nonlinear generalization of Perron-Frobenius theory and periodic points of nonexpansive maps. Recent Developments in Optimization and Nonlinear Analysis (Y. Censor and S. Reich, ed.). Contemporary Mathematics, vol. 204, American Math. Society, Providence, R.I., 1997, pp. 183-198.
15. R.D. Nussbaum and M. Scheutzow. Admissible arrays and periodic points of nonexpansive maps. Journal of the London Math. Soc. (to appear).
16. R.D. Nussbaum and S.M. Verduyn Lunel. Generalizations of the Perron-Frobenius theorem for nonlinear maps. Memoirs of the Amer. Math. Soc. (to appear).
17. 1-spaces. European J. Combinatorics 9 (1988), 73-81.
18. 1-spaces. European J. Combinatorics 12 (1991), 183.
19. R. Sine. A nonlinear Perron-Frobenius theorem. Proc. Amer. Math. Soc. 109 (1990), 331-336.
20. D. Weller. Hilbert's metric, part metric and self mappings of a cone. Ph.D. dissertation, Univ. of Bremen, Germany (1987).