Access the full text.
Sign up today, get DeepDyve free for 14 days.
K. Alfriend (1971)
Stability of and motion aboutL4 at three-to-one commensurabilityCelestial mechanics, 4
A.G. Sokol’ski (1977)
On Stability of an Autonomous Hamiltonian System with Two Degrees of Freedom under First-Order ResonancePrikl. Mat. Mekh., 41
(2001)
On the Problem of the Stability of the Equilibrium Position of a Hamiltonian System at Resonance 3 : 1, Prikl
A.G. Sokol’ski (1974)
On the Stability of an Autonomous Hamiltonian System with Two Degrees of Freedom in the Case of Equal FrequenciesPrikl. Mat. Mekh., 38
A. Elipe, V. Lanchares, T. López-Moratalla, A. Riaguas (2001)
Nonlinear Stability in Resonant Cases: A Geometrical ApproachJ. Nonlinear Sci., 11
A. Elipe, V. Lanchares, A. Pascual (2005)
On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under ResonancesJournal of Nonlinear Science, 15
C. L. Siegel, L. K. Moser (1971)
Lectures on Celestial Mechanics
K. Alfriend (1971)
Stability and motion in two degree-of-freedom hamiltonian systems for two-to-one commensurabilityCelestial mechanics, 3
A. Sokol'skii (1974)
On the stability of an autonomous hamiltonian system with two degrees of freedom in the case of equal frequencies: PMM vol. 38, n≗5, 1974. pp. 791–799Journal of Applied Mathematics and Mechanics, 38
G. L. Dirichlet (1897)
Werke: Vol. 2
K. Meyer, D. Schmidt (1986)
The Stability of the Lagrange Triangular Point and a Theorem of ArnoldJournal of Differential Equations, 62
K. T. Alfriend (1971)
Stability of and Motion about L 4 at Three to One CommensurabilityCelestial Mech., 4
A. Sokol'skii (1977)
On stability of an autonomous Hamiltonian system with two degrees of freedom under first-order resonance: PMM vol. 41, n≗ 1, 1977, pp. 24–33Journal of Applied Mathematics and Mechanics, 41
H. Cabral, K. Meyer (1999)
Stability of equilibria and fixed points of conservative systemsNonlinearity, 12
G. Dirichlet
Über die Stabilität des Gleichgewichts.Crelle's Journal, 1846
A. Elipe, V. Lanchares, T. López-Moratalla, A. Riaguas, A. Elipe
Pre-publicaciones Del Seminario Matematico 2001 Non Linear Stability in Resonant Cases: a Geometrical Approach
Ana Lería (2005)
Sobre la estabilidad de sistemas hamiltonianos con dos grados de libertad bajo resonancias
(1961)
The Stability of the Equilibrium Position of a Hamiltonian System of Ordinary Differential Equations in the General Elliptic Case
J. Palacián, P. Yanguas (2000)
Reduction of Polynomial Planar Hamiltonians with Quadratic Unperturbed PartSIAM Rev., 42
A. Elipe (2000)
Complete reduction of oscillators in resonance p:qPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 61 6 Pt A
L. Lerman, A. Markova (2009)
On stability at the Hamiltonian Hopf BifurcationRegular and Chaotic Dynamics, 14
A.P. Markeev (1997)
On a Critical Case of Fourth-Order Resonance in a Hamiltonian System with One Degree of FreedomPrikl. Mat. Mekh., 61
A. Markeyev (1997)
The critical case of fourth-order resonance in a hamiltonian system with one degree of freedomJournal of Applied Mathematics and Mechanics, 61
A. P. Markeev (1968)
Stability of a Canonical System with Two Degrees of Freedom in the Presence of ResonancePrikl. Mat. Mekh., 32
G.D. Birkhoff (1966)
Dynamical Systems
We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under low order resonances. For resonances of order bigger than two there are several results giving stability conditions, in particular one based on the geometry of the phase flow and a set of invariants. In this paper we show that this geometric criterion is still valid for low order resonances, that is, resonances of order two and resonances of order one. This approach provides necessary stability conditions for both the semisimple and non-semisimple cases, with an appropriate choice of invariants.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 4, 2012
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.