Symplectic integration of Hamiltonian systems using polynomial maps [PDF]
Physics Letters A, 2001 In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose such a symplectic integration algorithm using polynomial map refactorization of the symplectic map representing the
Berg +27 more
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Polynomial and rational integrability of polynomial Hamiltonian systems
Electronic Journal of Differential Equations, 2012 Within the class of canonical polynomial Hamiltonian systems anti-symmetric under phase-space involutions, we generalize some results on the existence of Darboux polynomial and rational first integrals for "kinetic plus potential" systems to general ...
Jaume Llibre +2 more
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Effective descriptions of bosonic systems can be considered complete [PDF]
Nature CommunicationsBosonic statistics give rise to remarkable phenomena, from the Hong–Ou–Mandel effect to Bose–Einstein condensation, with applications spanning fundamental science to quantum technologies. Modeling bosonic systems relies heavily on effective descriptions:
Francesco Arzani +2 more
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Darboux polynomials and first integrals of natural polynomial Hamiltonian systems [PDF]
Physics Letters A, 2004 We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function.
Maciejewski, Andrzej J. +1 more
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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
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Limit Cycles of a Class of Perturbed Differential Systems via the First-Order Averaging Method
Complexity, 2021 By means of the averaging method of the first order, we introduce the maximum number of limit cycles which can be bifurcated from the periodic orbits of a Hamiltonian system.
Amor Menaceur +4 more
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Linearizability of planar polynomial Hamiltonian systems
Nonlinear Analysis: Real World Applications, 2022 Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system.
Barbara Arcet +2 more
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On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D [PDF]
Theoretical and Applied Mechanics, 2017 The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials.
Esen Oğul +2 more
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Solving systems of Boolean multivariate equations with quantum annealing
Physical Review Research, 2022 Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based postquantum cryptography, coding theory, and computer algebra.
Sergi Ramos-Calderer +6 more
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Complete commutative subalgebras in polynomial poisson algebras: A proof of the Mischenko-Fomenko conjecture [PDF]
Theoretical and Applied Mechanics, 2016 The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra g there exists a complete set of commuting polynomials on its dual space g*.
Bolsinov Alexey V.
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