Isochronicity and linearizability of planar polynomial Hamiltonian systems
Journal of Differential Equations, 2015 Agraïments: UNAB13-4E-1604. The second author is supported by the Slovenian Research Agency. Both authors are supported by the grant FP7-PEOPLE-2012-IRSES-316338. We also thank the referee for valuable remarks which helped to improve the manuscript. In this paper we study isochronicity and linearizability of planar polynomial Hamiltonian systems. First
Jaume Llibre, Valery G. Romanovski
exaly +10 more sources
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
openaire +5 more sources
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
openaire +6 more sources
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.
openaire +2 more sources
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
doaj +1 more source
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
core +2 more sources
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
doaj +1 more source
Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems [PDF]
, 2009 One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself.
Abramovitz +21 more
core +1 more source
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.
openaire +4 more sources
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.
core +3 more sources