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A. Tsiganov (2007)
Darboux-Nijenhuis variables for open generalized Toda chainsTheoretical and Mathematical Physics, 152
V. B. Kuznetsov, A.V. Tsiganov (1989)
Infinite Series Algebras Lie and Boundary Conditions for the Integrable SystemsZap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 172
A.V. Tsiganov (2007)
A Family of the Poisson Brackets Compatible with the Sklyanin BracketJ. Phys. A: Math. Gen., 40
A.V. Tsiganov (2001)
The Maupertuis Principle and Canonical Transformations of the Extended Phase SpaceJ. Nonlinear Math. Phys., 8
E.K. Sklyanin (1985)
The Quantum Toda ChainLecture Notes in Phys., 226
A. Tsiganov (2007)
The Poisson bracket compatible with the classical reflection equation algebraRegular and Chaotic Dynamics, 13
(2000)
Journal of Nonlinear Mathematical Physics 2001, V.8, N 1, 157–182 Review Article The Maupertuis Principle and Canonical Transformations of the Extended Phase Space
A. Tsiganov (1998)
DYNAMICAL BOUNDARY CONDITIONS FOR INTEGRABLE LATTICESJournal of Physics A, 31
M. Karlovini, G. Pucacco, K. Rosquist, L. Samuelsson (1998)
A unified treatment of quartic invariants at fixed and arbitrary energyJournal of Mathematical Physics, 43
E. Sklyanin (1988)
Boundary conditions for integrable quantum systemsJournal of Physics A, 21
A. Tsiganov (1999)
Properties of the canonical transformations of the time for the Toda lattice and the Henon-Heiles systemJournal of Physics A, 33
A. Tsiganov (1999)
Canonical transformations of the extended phase space, Toda lattices and the Stäckel family of integrable systemsJournal of Physics A, 33
E. Sklyanin (1987)
The quantum Toda chainPhysica D: Nonlinear Phenomena, 28
A. Motter, K. Gelfert (2009)
Time-metric equivalence and dimension change under time reparameterizations.Physical review. E, Statistical, nonlinear, and soft matter physics, 79 6 Pt 2
A.V. Tsiganov (2007)
On the Two Different Bi-Hamiltonian Structures for the Toda LatticeJ. Phys. A: Math. Gen., 40
A. Tsiganov (2006)
A family of the Poisson brackets compatible with the Sklyanin bracketJournal of Physics A: Mathematical and Theoretical, 40
H. Yehia (2006)
The master integrable two-dimensional system with a quartic second integralJournal of Physics A: Mathematical and General, 39
A. Reyman, M. Semenov-Tian-Shansky (1979)
Reduction of Hamiltonian systems, affine Lie algebras and Lax equationsInventiones mathematicae, 54
A. Tsiganov (2007)
On two different bi-Hamiltonian structures for the Toda latticeJournal of Physics A: Mathematical and Theoretical, 40
Андрей Цыганов, Andrey Tsiganov (2007)
О переменных Дарбу - Нийенхейса для открытых обобщенных цепочек Тоды@@@Darboux - Nijenhuis variables for open generalized Toda chains, 152
O. Bogoyavlensky (1976)
On perturbations of the periodic Toda latticeCommunications in Mathematical Physics, 51
A.V. Tsiganov (2000)
Canonical Transformations of the Extended Phase Space, Toda Lattices and Stäckel SystemsJ. Phys. A: Math. Gen., 33
A. Tsiganov (1996)
The Kowalewski top: A new Lax representationJournal of Mathematical Physics, 38
A. Borisov, I. Mamaev (2008)
Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systemsRegular and Chaotic Dynamics, 13
We discuss some special classes of canonical transformations of the time variable, which relate different integrable systems. Such dual systems have different integrals of motion, Lax equations, separated variables and bi-hamiltonian structures. As an example the two-dimensional periodic Toda lattices associated with the classical root systems and the dual natural systems on the palne are considered in detail.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 26, 2009
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