Access the full text.
Sign up today, get DeepDyve free for 14 days.
(2006)
Classification of Birkhoff-Integrable Generalized Toda Lattices
P.A. Damianou (1994)
Multiple Hamiltonian Structures for Toda-Type Systems: Topology and PhysicsJ. Math. Phys., 35
P.A. Damianou (2000)
Multiple Hamiltonian Structures for Toda Systems of type A-B-C: Sophia Kovalevskaya to the 150th anniversaryRegul. Chaotic Dyn., 5
H. Rugh (1999)
SYMMETRIES, TOPOLOGY, AND RESONANCES IN HAMILTONIAN MECHANICS (Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 31)Bulletin of The London Mathematical Society, 31
M. Pedroni, P. Vanhaecke (2007)
A Lie algebraic generalization of the Mumford system, its symmetries and its multi-Hamiltonian structure
P. Deift, L. Li, T. Nanda, C. Tomei (1984)
The Toda flow on a generic orbit is integrableBulletin of the American Mathematical Society, 11
M. Adler, P. Moerbeke, P. Vanhaecke (2004)
Algebraic Integrability, Painlevé Geometry and Lie Algebras
Djagwa Dehainsala (2011)
Algebraic Integrability and Geometry of the d (2) Toda Lattice
(1974)
The Toda Lattice: 1
Patrice Tauvel, R. Yu (2004)
Indice et formes linaires stables dans les algbres de LieJournal of Algebra
A. Tsiganov (2009)
Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motionRegular and Chaotic Dynamics, 14
P. Damianou (2007)
MULTIPLE HAMILTONIAN STRUCTURES FOR TODA SYSTEMS OF TYPE A � B � C
N.M. Ercolani, H. Flaschka, S. Singer (1993)
The Verdier Memorial Conference on Integrable Systems: Actes du Colloque International de Luminy (1991)
B. Kostant (1979)
The solution to a generalized Toda lattice and representation theoryAdvances in Mathematics, 34
O. Bogoyavlensky (1976)
On perturbations of the periodic Toda latticeCommunications in Mathematical Physics, 51
N. Ercolani, H. Flaschka, S. Singer (1993)
The Geometry of the Full Kostant-Toda Lattice
M. Olshanetsky, A. Perelomov (1979)
Explicit solutions of classical generalized toda modelsInventiones mathematicae, 54
P. Damianou (1994)
Multiple Hamiltonian Structures for Toda-type systemsarXiv: Mathematical Physics
D. Dehainsala (2011)
Algebraic Integrability and Geometry of the d3 (2) Toda LatticeRegul. Chaotic Dyn., 16
M. Adler, P. Moerbeke (1980)
Completely Integrable Systems, Euclidean Lie-algebras, and CurvesAdvances in Mathematics, 38
P. Damianou, H. Sabourin, P. Vanhaecke (2012)
Height-2 Toda systems, 1460
A. Borisov, I. Mamaev (2004)
Necessary and sufficient conditions for the polynomial integrability of generalized Toda chainsDoklady Mathematics, 69
(1974)
Conjugaison des sous-algèbres d’isotropie
H. Flaschka (1974)
The Toda Lattice: 1. Existence of IntegralsPhys. Rev. B (3), 9
A. Veselov, A. Penskoi (2000)
On algebro-geometric Poisson brackets for the Volterra latticearXiv: Mathematical Physics
O. Bogoyavlenskij (2008)
Integrable Lotka-Volterra systemsRegular and Chaotic Dynamics, 13
V. Kozlov, D. Treshchev (1990)
POLYNOMIAL INTEGRALS OF HAMILTONIAN SYSTEMS WITH EXPONENTIAL INTERACTIONMathematics of The Ussr-izvestiya, 34
P. Deift, L. C. Li, T. Nanda, C. Tomei (1986)
The Toda Flow on a Generic Orbit Is IntegrableComm. Pure Appl. Math., 39
M. Adler, P. Moerbeke, P. Vanhaecke (2004)
Ergeb. Math. Grenzgeb. (3)
A. Borisov, I. Mamaev (2012)
Two non-holonomic integrable problems tracing back to ChaplyginRegular and Chaotic Dynamics, 17
A. V. Borisov, I. S. Mamaev (2004)
Necessary and Sufficient Conditions for the Polynomial Integrability of Generalized Toda ChainsDokl. Akad. Nauk, 394
V. Kozlov (1996)
Symmetries, topology and resonances in Hamiltonian mechanics
A.V. Borisov, I. S. Mamaev (2006)
Topological Methods in the Theory of Integrable Systems
P.A. Damianou, H. Sabourin, P. Vanhaecke (2011)
Group Analysis of Differential Equations and Integrable Systems
P. Damianou, V. Papageorgiou (2007)
On an integrable case of Kozlov-Treshchev Birkhoff integrable potentialsRegular and Chaotic Dynamics, 12
Paola Cellini, P. Papi (2006)
ad-Nilpotent Ideals of a Borel Subalgebra
We construct a large family of Hamiltonian systems which interpolate between the classical Kostant-Toda lattice and the full Kostant-Toda lattice and we discuss their integrability. There is one such system for every nilpotent ideal I in a Borel subalgebra b+ of an arbitrary simple Lie algebra g. The classical Kostant-Toda lattice corresponds to the case of I = [n+, n+], where n+ is the unipotent ideal of b+, while the full Kostant-Toda lattice corresponds to I = {0}. We mainly focus on the case I = [[n+, n+], n+]. In this case, using the theory of root systems of simple Lie algebras, we compute the rank of the underlying Poisson manifolds and construct a set of (rational) functions in involution, large enough to ensure Liouville integrability. These functions are restrictions of well-chosen integrals of the full Kostant-Toda lattice, except for the case of the Lie algebras of type C and D where a different function (Casimir) is needed. The latter fact, and other ones listed in the paper, point at the Liouville integrability of all the systems we construct, but also at the nontriviality of obtaining the result in full generality.
Regular and Chaotic Dynamics – Springer Journals
Published: Jun 17, 2015
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.