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Reduction of Polynomial Planar Hamiltonians with Quadratic Unperturbed Part

• Jesús F. Palacián, Patricia Yanguas
• SIAM Review
• 2000

We classify the possible normal forms of quadratic Hamiltonians in 2 dimensions. Then we give a method to reduce by one the number of degrees of freedom of an arbitrary polynomial Hamiltonian whose… (More)

On Perturbed Oscillators in 1 - 1 - 1 Resonance : The Case of Axially Symmetric Cubic

• Patricia Yanguas
• 2001

Axially symmetric perturbations of the isotropic harmonic oscillator in three dimensions are studied. A normal form transformation introduces a second symmetry, after truncation. The reduction of the… (More)

Lowering the dimension of polynomial vector fields in R(2) and R(3).

• Patricia Yanguas
• Chaos
• 2001

We classify the normal forms associated to polynomial vector fields with dimensions two and three whose principal part is linear. Then we reduce by one the dimension of the associated differential… (More)

Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem

• Patricia Yanguas, Jesús F. Palacián, Kenneth R. Meyer, H. Scott Dumas
• SIAM J. Applied Dynamical Systems
• 2008

Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori

• Kenneth R. Meyer, Jesús F. Palacián, Patricia Yanguas
• SIAM J. Applied Dynamical Systems
• 2011

We investigate the dynamics of various problems defined by Hamiltonian systems of two and three degrees of freedom that have in common that they can be reduced by an axial symmetry. Specifically, the… (More)

A Universal Procedure for Normalizing n-Degree-of-Freedom Polynomial Hamiltonian Systems

• Susana Gutiérrez-Romero, Jesús F. Palacián, Patricia Yanguas
• SIAM Journal of Applied Mathematics
• 2005

We depart from an n-degree-of-freedom Hamiltonian formed by the sum of homogeneous polynomials in n coordinates and n momenta with arbitrary coefficients. By extending formally an integral of the… (More)

Approximating the Invariant Sets of a Finite Straight Segment near Its Collinear Equilibria

• Jesús F. Palacián, Patricia Yanguas, Susana Gutiérrez-Romero
• SIAM J. Applied Dynamical Systems
• 2006

Periodic orbits of the Lorenz System through perturbation Theory

• Jesús F. Palacián, Patricia Yanguas
• I. J. Bifurcation and Chaos
• 2001

Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame

• Manuel Iñarrea, Víctor Lanchares, Jesús F. Palacián, Ana I. Pascual, J. P. Salas, Patricia Yanguas
• Applied Mathematics and Computation
• 2015

In this paper we focus on a generalized Hénon–Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability… (More)

Hamiltonian Oscillators in 1 - 1 - 1 Resonance: Normalization and Integrability

• Sebastián Ferrer, Jesús F. Palacián, Patricia Yanguas
• J. Nonlinear Science
• 2000

We consider a family of three-degree-of-freedom (3-DOF) Hamiltonian systems defined by a Taylor expansion around an elliptic equilibrium. More precisely, the system is a perturbed harmonic oscillator… (More)

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