Rotation number associated with difference equations satisfied by polynomials orthogonal on the unit circle

Journal of Differential Equations

Volumn 132, Issue 1, 1996, Pages 140-178

  Geronimo, J S ^a   Johnson, R A ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030595783     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0175     Document Type: Article

References (30)

1. 1. F. Atkinson, "Discrete and Continuous Boundary Value Problems," Academic Press, New York, 1964.
2. 2. J. Avron and B. Simon, Almost periodic Schrödinger operators. II. The integrated density of states, Duke Math. J. 50 (1983), 369-391.
3. 3. A. M. Bruckstein and T. Kailath, Inverse scattering for discrete transmission-line models, SIAM Rev. 29 (1987), 359-390.
4. 4. K. P. Bube and Robert Burridge, The one-dimensional inverse problem of reflection seismology, SIAM Rev. 25 (1983), 497-559.
5. 5. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin, 1978.
6. 6. W. Craig and B. Simon, Subharmonicity of the Lyapunov index, Duke Math. J. 50 (1983), 551-560.
7. 7. C. De Concini and R. Johnson, The algebraic - geometric AKNS potentials, Ergodic Theory Dynam. Systems 1 (1987), 1-24.
8. 8. R. Ellis, "Lectures on Topological Dynamics," Benjamin, New York, 1967.
9. 9. J. Geronimo, Polynomials orthogonal on the unit circle with random recurrence coefficients, in "Proceedings, US - USSR Conference on Approximation Theory, St. Petersburg, Russia," Lecture Notes in Mathematics, Vol. 1550, Springer-Verlag, Berlin/New York.
10. 10. J. S. Geronimo and R. Johnson, An inverse problem associated with polynomials orthogonal on the unit circle, in preparation.
11. 11. J. Geronimo and A. Teplaev, A difference equation arising from the trigonometric moment problem having random reflection coefficients, an operator theoretic approach, J. Funct. Anal. 123 (1994), 12-45.
12. 12. Y. Geronimus, "Polynomials Orthogonal on a Circle and Interval," Pergamon, New York, 1960.
13. 13. M. Herman, Une méthode pour meriorer les exponents de Lyapounov et quelques exemples montront le caractère local d'une théorème de Arnold et de Moser sur le tore de dimension 2, Comm. Math. Helv. 58 (1983), 453-502.
14. 14. K. Ishii, Localization of eigenstates and transport phenomena in one-dimensional disordered systems, Progr. Theor. Phys. Suppl. 53 (1973), 77-118.
15. 15. R. Johnson, m-functions and Floquet exponents for linear differential systems, Ann. Mat. Pura Appl. 147 (1987), 211-248.
16. 16. R. Johnson, Remarks on linear differential systems with measurable coefficients, Proc. A.M.S. 100 (1987), 491-504.
17. 17. R. Johnson and J. Moser, The rotation number for almost-periodic potentials, Comm. Math. Phys. 84 (1982), 403-438.
18. 18. R. Johnson and M. Nerurkar, Exponential dichotomy and rotation number for linear Hamiltonian systems, J. Differential Equations 108 (1994), 201-216.
19. 19. R. Johnson, K. Palmer, and G. Sell, Ergodic properties of linear dynamical systems, SIAM J. Math. Anal. 18 (1987), 1-33.
20. 20. S. Kotani, Lyapounov indices determine absolutely continuous spectra of stationary one-dimensional random Schrödinger operators, in "Stochastic Analysis" (K. Ito, Ed.), pp. 225-247, North-Holland, Amsterdam, 1984.
21. 21. U. Krengel, "Ergodic Theorem," De Gruyter, New York, 1985.
22. 22. V. Oseledec, A multiplicative ergodic theorem: Lyapounov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197-231.
23. 23. K. Palmer, Exponential dichotomies, the shadowing lemma, and transversal homoclinic points, Dynamics Reported 1 (1988), 265-305.
24. 24. L. Pastur, Spectral properties of disordered systems in the one-body approximation, Comm. Math. Phys. 75 (1980), 179-196.
25. 25. E. A. Robinson and S. Treitel, "Geophysical Signal Analysis," Prentice-Hall, Englewood Cliffs, NJ, 1980.
26. 26. D. Ruelle, Ergodic theory of differential dynamical systems, Publ. Inst. Hautes Etudes Sci. 50 (1979), 275-320.
27. 27. R. Sacker and G. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), 320-358.
28. 28. S. Schwartzmann, Asymptotic cycles, Ann. Math. 66 (1957), 270-284.
29. 29. J. Selgrade, Isolated invariant sets for flows on vector bundles, Trans. Amer. Math. Soc. 203 (1975), 359-390.
30. 30. F. Sun and M. Qian, Lyapounov exponent and rotation number for stochastic Dirac operators, Acta Math. Appl. Sin. 8 (1992), 333-347.