Solution of the Boolean Markus-Yamabe problem

Advances in Applied Mathematics

Volumn 22, Issue 1, 1999, Pages 60-102

  Shih, Mau Hsiang ^a   Ho, Juei Ling ^b  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b Tainan Woman's College of Arts and Technology   (Taiwan)

Author keywords

Content addressable memory; Boolean matrix; Boolean dynamical system; global attractor; eigenvalue; spectral radius; von Neumann neighborhood; Hamming distance; Markus Yamabe conjecture; automata network

Indexed keywords

EID: 0032662009     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1998.0622     Document Type: Article

References (24)

1. Baclawski K., Björner A. Fixed points in partially ordered sets. Adv. in Math. 31:1979;263-287.
2. Baclawski K. Combinatorics: Trends and examples. New Directions in Applied Mathematics. 1986;Springer-Verlag, Berlin-Heidelberg-New York.
3. Barabanov N. E. On the Kalman's problem. Sibirsk. Mat. Zh. 29:1988;2-11.
4. Bernet J., Llibre J. Counterexample to Kalman and Markus-Yamabe conjecture in larger than 3. Dynamics Continuous, Discrete Impulsive Syst. 2:1996;337-379.
5. Brualdi R. A., Ryser H. J. Combinatorial Matrix Theory. 1991;Cambridge Univ. Press, Cambridge.
6. A. Cima, A. Gasull, F. Mañosas, The discrete Markus-Yamabe problem, Universitat Autõnoma de Barcelona, 1995.
7. Cima A., van den Essen A., Gasull A., Hubbers E., Mañosas F. A polynomial counterexample to the Markus-Yamabe conjecture. Adv. in Math. 131:1997;453-457.
8. van den Essen A., Hubbers E. Chaotic polynomial automorphisms; counterexamples to several conjectures. Adv. in Appl. Math. 18:1997;382-388.
9. Fessler R. A solution of the two dimensional global asymptotic stability conjecture. Ann. Polon. Math. 62:1995;45-74.
10. Gale D., Nikaido H. The Jacobian matrix and global univalence of mappings. Math. Ann. 159:1965;81-93.
11. Glutsyuk A. A. A complete solution of the Jacobian problem for vector fields on the plane. Russian Math. Surveys. 49:1994;185-186.
12. Goles E., Martinez S. Neural and Automata Networks, Dynamical Behavior and Applications. 1991;Kluwer Academic, Dordrecht-Boston-London.
13. Gutierrez C. A solution to the bidimensional global asymptotic stability conjecture. Ann. Inst. H. Poincaré Anal. Non Linéaire. 12:1995;627-671.
14. Hopfield J. J. Neural network and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. U.S.A. 79:1982;2554-2558.
15. Kohonen T. Self-Organization and Associative Memory. Springer Series in Information Sciences. 1984;Springer-Verlag, Berlin-Heidelberg-New York.
16. LaSalle J. P. The Stability of dynamical systems. SIAM, Regional Conference Series in Applied Mathematics. 1976.
17. Markus L., Yamabe H. Global stability criteria for differential systems. Osaka Math. J. 126:1960;305-317.
18. Meisters G. H., Olech C. Solution of the Global Asymptotic Stability Jacobian Conjecture for the Polynomial Case. Analyse Mathématique et Applications. 1988;Gauthier-Villars, Paris. p. 373-381.
19. Nikaido H. Convex Structures and Economic Theory. 1968;Academic Press, New York.
20. Prather R. E. Discrete Mathematical Structures for Computer Science. 1976;Houghton Mifflin, Boston.
21. Robert F. Itérations sur des ensembles finis et automates cellulaires contractants. Linear Algebra Appl. 29:1980;393-412.
22. Robert F. Dérivée discrite et convergence local d'une iteration booléenne. Linear Algebra Appl. 52:1983;547-589.
23. Robert F. Discrete Iterations, A Metric Study. Springer Series in Computational Mathematics. 1986;Springer-Verlag, Berlin-Heidelberg-New York.
24. von Neumann J. Burks A. W. Theory of Self-Reproducing Automata. 1966;Univ. of Illinois Press, Champaign.