Uniform Weak Disconjugacy and Principal Solutions for Linear Hamiltonian Systems
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The paper analyzes the property of (uniform) weak disconjugacy for nonautonomous linear Hamiltonian systems, showing that it is a convenient replacement for the more restrictive property of disconjugacy. In particular, its occurrence ensures the existence of principal solutions. The analysis of the properties of these solutions provides ample information about the dynamics induced by the Hamiltonian system on the Lagrange bundle.
KeywordsNonautonomous linear Hamiltonian systems Uniform weak disconjugacy Principal solutions
Partly supported by MIUR (Italy), by MEC (Spain) under project MTM2012-30860, and by JCyL (Spain) under project VA118A12-1.
- 1.Coppel, W.A.: Disconjugacy. Lecture Notes in Mathematics 220, Springer, Berlin/Heidelberg, New York (1971)Google Scholar
- 3.Fabbri, R., Johnson, R., Núñez, C.: Rotation number for non-autonomous linear Hamiltonian systems I: Basic properties. Z. Angew. Math. Phys. 53, 484–502 (2002)Google Scholar
- 4.Fabbri, R., Johnson, R., Núñez, C.: On the Yakubovich Frequency Theorem for linear non-autonomous control processes. Discrete Contin. Dynam. Systems, Ser. A 9(3), 677–704 (2003)Google Scholar
- 8.Johnson, R., Nerurkar, M.: Controllability, stabilization, and the regulator problem for random differential systems. Mem. American Mathematical Society, vol. 646, American Mathematical Society, Providence, RI (1998)Google Scholar
- 11.Johnson, R., Núñez, C.: Remarks on linear-quadratic dissipative control systems. Discrete Contin. Dynam. Systems, Ser. B, to appear.Google Scholar
- 14.Lidskiĭ, V.B.: Oscillation theorems for canonical systems of differential equations. Dokl. Akad. Nank. SSSR 102, 877–880 (1955) (English translation in: NASA Technical Translation, P-14, 696)Google Scholar
- 17.Reid, W.T.: Sturmian theory for ordinary differential equations. Applied Mathematical Sciences, vol. 31, Springer, New York (1980)Google Scholar
- 19.Yakubovich, V.A.: Oscillatory properties of the solutions of canonical equations. Amer. Math. Soc. Transl. Ser. 2 42, 247–288 (1964)Google Scholar