Results 191 to 200 of about 77,468 (213)

Dynamics and Periodic Solutions in Cubic Polynomial Hamiltonian Systems

Qualitative Theory of Dynamical Systems, 2018
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Dante Carrasco-Olivera, Claudio Vidal
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Isochronicity of plane polynomial Hamiltonian systems

Nonlinearity, 1997
Polynomial Hamiltonian systems in the plane are studied which can have isochronous center singular points. More exactly, the author deals with a complex extension of the related system and closed vanishing cycles \(\gamma (h)\) on the complex Riemannian surface \(H^{-1}(h)=\{H=h\}\) being a complexification of the corresponding closed periodic orbit ...
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Polynomial Integrals of Hamiltonian Systems

1996
In this chapter we present specific methods of searching for Hamiltonian systems which admit first integrals polynomial in momenta. This problem is actual because in Hamiltonian mechanics the majority of known integrals are either polynomials in momenta or functions of these polynomials (see §1 of Chap. II).
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Non-isochronicity of the center in polynomial Hamiltonian systems

Nonlinear Analysis: Theory, Methods & Applications, 2010
The authors study the problem of isochronicity for polynomial Hamiltonian systems with the Hamiltonian \[ H(x,y)=\frac{x^2+y^2}2+\sum_{i+j=m}^na_{ij}x^i y^j, \tag{1} \] where \(x,y,a_{ij}\in \mathbb{R}, \;\sum_{i+j=m}a_{ij}^2\neq 0\), \(m, n \in \mathbb{N}\) and \(n\geq m \geq 3\). Let \(M_k= \sum_{i=0}^k a_{2 k -2 i, 2i} w_{i,k-i} \), where \[ w_{ij}=\
Wang, Zhaoxia, Chen, Xingwu, Zhang, Weinian   +2 more
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Integrable Hamiltonian systems related to the polynomial eigenvalue problem

Journal of Mathematical Physics, 1990
The independent integrals of motion in involution for the Hamiltonian system related to the second-order polynomial eigenvalue problem are constructed by using relevant recursion formula. The hierarchy of Hamiltonian systems obtained from the above problem and the time part of the Lax pair are shown to be completely integrable and they are shown to ...
Zeng, Yunbo, Li, Yishen
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Incomplete integrable Hamiltonian systems with complex polynomial Hamiltonian of small degree

Sbornik: Mathematics, 2010
Complex Hamiltonian systems with one degree of freedom on with the standard symplectic structure and a polynomial Hamiltonian function , , are studied. Two Hamiltonian systems , , are said to be Hamiltonian equivalent if there exists a complex symplectomorphism taking the vector field to . Hamiltonian equivalence classes of systems are described in the
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Polynomial first integrals of Hamiltonian systems with exponential interaction

Functional Analysis and Its Applications, 1991
Consider a Hamiltonian of the form \[ H=T+V,\qquad T={1\over 2}\sum^ n_{i,j=1}a_{i,j}y_ iy_ j,\qquad V=\sum_{m\in Z^ n}v_ m\exp(m,x) \] where \((a_{i,j})\) is a nondegenerate constant matrix \(v_ m=\text{const}\), \(x=(x_ 1,\dots,x_ n)\) and \(y=(y_ 1,\dots,y_ n)\) are conjugate canonical variables.
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Planar polynomial Hamiltonian differential systems with global centers

SCIENTIA SINICA Mathematica, 2021
He Hongjin, Llibre Jaume, Xiao Dongmei
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Uncertainty quantification for random Hamiltonian systems by using polynomial expansions and geometric integrators

Chaos, Solitons and Fractals, 2021
Marc Jornet
exaly  

Polynomial and Rational First Integrals for Non–Autonomous Polynomial Hamiltonian Systems

Dynamic Systems and Applications, 2020
Azucena Caicedo, Jaume Llibre, Claudio Vidal   +2 more
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