49 citations · 177 across the 10 of their papers we have counts for
5 papers · 1 filter
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…
Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps
H. E. Lomeli, J. D. Meiss
We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation throu…