Multiple partial integrals of polynomial Hamiltonian systems
Acta et commentationes: Ştiinţe Exacte şi ale Naturii, 2022 We consider an autonomous real polynomial Hamiltonian ordinary differential system. Sufficient conditions for the construction of additional first integrals on polynomial partial integrals and multiple polynomial partial integrals are obtained. Classes of autonomous polynomial Hamiltonian ordinary differential systems with first integrals which ...
Andrei Pranevich +2 more
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The Number of Limit Cycles Bifurcating from an Elementary Centre of Hamiltonian Differential Systems
Mathematics, 2022 This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function H=12y2+12x2−23x3+a4x4(a≠0) under two types of polynomial perturbations of degree m ...
Lijun Wei, Yun Tian, Yancong Xu
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A finite-dimensional integrable system associated with a polynomial eigenvalue problem
International Journal of Mathematics and Mathematical Sciences, 2006 M. Antonowicz and A. P. Fordy (1988) introduced the second-order polynomial eigenvalue problem Lφ=(∂2+∑i=1nviλi)φ=αφ(∂=∂/∂x,α=constant) and discussed its multi-Hamiltonian structures.
Taixi Xu, Weihua Mu, Zhijun Qiao
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Hamiltonian elliptic systems with critical polynomial-exponential growth
Nonlinear Analysis, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
João Marcos do Ó +2 more
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Legendre Polynomials Spectral Approximation for the Infinite‐Dimensional Hamiltonian Systems [PDF]
Mathematical Problems in Engineering, 2011 This paper considers a Legendre polynomials spectral approximation for the infinite‐dimensional Hamiltonian systems. As a consequence, the Legendre polynomials spectral semidiscrete system is a Hamiltonian system for the Hamiltonian system whose Hamiltonian operator is a constant differential operator.
Lv, Zhongquan, Xue, Mei, Wang, Yushun
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Multi-Objective Robust Control for Vehicle Active Suspension Systems via Parameterized Controller
IEEE Access, 2020 A parameterized controller design approach is proposed to solve the problem of multi-objective control for vehicle active suspension systems by using symbolic computation.
Zhong Cao +3 more
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Polynomial entropies for Bott nondegenerate Hamiltonian systems
, 2012 In this paper, we study the entropy of a Hamiltonian flow in restriction to an enregy level where it admits a first integral which is nondegenerate in the Bott sense. It is easy to see that for such a flow, the topological entropy vanishes. We focus on the polynomial and the weak polynomial entropies.
Labrousse, Clémence, Marco, Jean-Pierre
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Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties [PDF]
, 2007 A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible ...
Bôcher M. +5 more
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Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
, 1998 The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studies for systems derived from a rational Lax function.
I. A. B. Strachan, Kupershmidt B. A.
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A multiprover interactive proof system for the local Hamiltonian problem [PDF]
, 2014 We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits to each prover,
Fitzsimons, Joseph, Vidick, Thomas
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