scholarly journals Ergodic Properties and Rotation Number for Linear Hamiltonian Systems

1998 ◽  
Vol 148 (1) ◽  
pp. 148-185 ◽  
Author(s):  
Sylvia Novo ◽  
Carmen Núñez ◽  
Rafael Obaya
Keyword(s):  
Hamiltonian Systems ◽  
Rotation Number ◽  
Ergodic Properties ◽  
Linear Hamiltonian Systems

Ergodic properties and Weyl M-functions for random linear Hamiltonian systems

2000 ◽  
Vol 130 (5) ◽  
pp. 1045-1079 ◽  
Author(s):  
R. Johnson ◽  
S. Novo ◽  
R. Obaya
Keyword(s):  
Hamiltonian Systems ◽  
Qualitative Description ◽  
Invariant Region ◽  
Absolutely Continuous ◽  
Hamiltonian Equations ◽  
Radial Limits ◽  
Ergodic Properties ◽  
Ergodic Measures ◽  
Linear Hamiltonian Systems ◽  
Dynamical Information

This paper provides a topological and ergodic analysis of random linear Hamiltonian systems. We consider a class of Hamiltonian equations presenting absolutely continuous dynamics and prove the existence of the radial limits of the Weyl M-functions in the L1-topology. The proof is based on previous ergodic relations obtained for the Floquet coefficient. The second part of the paper is devoted to the qualitative description of disconjugate linear Hamiltonian equations. We show that the principal solutions at ±∞ define singular ergodic measures, and determine an invariant region in the Lagrange bundle which concentrates the essential dynamical information. We apply this theory to the study of the n-dimensional Schrödinger equation at the first point of the spectrum.

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