Results 11 to 20 of about 77,468 (213)
On the 16th Hilbert Problem for Discontinuous Piecewise Polynomial Hamiltonian Systems
Journal of Dynamics and Differential Equations, 2021 In this paper we study the maximum number of limit cycles of the discontinuous piecewise differential systems with two zones separated by the straight line y = 0, in y ≥ 0 there is a polynomial Hamiltonian system of degree m, and in y ≤ 0 there is a polynomial Hamiltonian system of degree n.
Tao Li, Jaume Llibre
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Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree −2 [PDF]
Physics Letters A, 2011 Agraïments: The third author is partially supported by FCT through CAMGDS, Lisbon. We characterize the analytic integrability of Hamiltonian systems with Hamiltonian H = 1/ 2 2∑ i=1 p 2 i + V (q1, q2), having homogeneous potential V (q1, q2) of degree −2.
Llibre, Jaume +2 more
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POLYNOMIAL INTEGRALS OF HAMILTONIAN SYSTEMS WITH EXPONENTIAL INTERACTION [PDF]
Mathematics of the USSR-Izvestiya, 1990 The Hamiltonian systems studied in this paper are those of the form \[ \dot x=Ay,\quad \dot y=-\sum^{m}_{k=1}[v_ k \exp a_ k(x)]a_ k, \] where \(0\neq v_ k\in {\mathbb{R}}\), \(0\neq a_ k\in W^*\) for some linear vector space \(W^ n\), \(x\in W\), and A: \(W^*\to W\) is the isomorphism associated with a scalar product in W.
Kozlov, V. V., Treshchev, D. V.
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Determining a local Hamiltonian from a single eigenstate [PDF]
Quantum, 2019 We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian. We present evidence that the answer is ``yes" for generic local Hamiltonians, given either the ground state or an excited ...
Xiao-Liang Qi, Daniel Ranard
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On a computer-aided approach to the computation of Abelian integrals [PDF]
, 2011 An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems.
A. Neumaier +27 more
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Intractability of Electronic Structure in a Fixed Basis
PRX Quantum, 2022 Finding the ground-state energy of electrons subject to an external electric field is a fundamental problem in computational chemistry. While the theory of QMA-completeness has been instrumental in understanding the complexity of finding ground states in
Bryan O’Gorman +3 more
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Polynomial Hamiltonian systems with movable algebraic singularities [PDF]
Journal d'Analyse Mathématique, 2016 The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic continuation along a rectifiable curve, are at most algebraic branch points.
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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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Asymptotic equality of the isolated and the adiabatic susceptibility [PDF]
, 1974 Many-particle systems with a hamiltonian of the form H = A + hB, h being a parameter, are discussed. In particular, for a certain class of these systems, a criterion is derived for the asymptotic equality of the isolated and the adiabatic susceptibility ...
Caspers, W.J., Valkering, T.P.
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