49 citations · 177 across the 10 of their papers we have counts for
11 papers
On Hamiltonian flows whose orbits are straight lines
Hans Koch, Héctor E. Lomelí
We consider real analytic Hamiltonians whose flow depends linearly on time. Trivial examples are Hamiltonians that do not depend on the coordinate . By a theorem of Mos…
Invariant manifolds for analytic difference equations
Rafael de la Llave, Hector E. Lomeli
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and…
Symmetry Reduction by Lifting for Maps
H. R. Dullin, H. E. Lomeli, J. D. Meiss
We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies…
Resonance Zones and Lobe Volumes for Volume-Preserving Maps
H. E. Lomelí, J. D. Meiss
We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes…
Generating Forms for Exact Volume-Preserving Maps
H. E. Lomelí, J. D. Meiss
We study the group of volume-preserving diffeomorphisms on a manifold. We develop a general theory of implicit generating forms. Our results generalize the classical formulas for g…
Canonical Melnikov theory for diffeomorphisms
H. E. Lomelí, J. D. Meiss, R. Ramírez-Ros
We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for…