Héctor E. Lomelí

Quadratic volume-preserving maps

We study quadratic, volume-preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area-preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume-preserving maps in three-space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.

Computation of Heteroclinic Arcs with Application to the Volume Preserving Henon Family

Let

Resonance zones and lobe volumes for exact volume-preserving maps

f:\mathbb{R}^3\rightarrow\mathbb{R}^3

Applications of the Melnikov method to twist maps in higher dimensions using the variational approach

be a diffeomorphism with

Saddle connections and heteroclinic orbits for standard maps

p_0,p_1\in\mathbb{R}^3

Heteroclinic orbits and Flux in a perturbed integrable Suris map

distinct hyperbolic fixed points. Assume that

Perturbations of elliptic billiards

W^u(p_0)

Heteroclinic bifurcations and chaotic transport in the two-harmonic standard map

and

Separatrix Splitting in 3D Volume-Preserving Maps

W^s(p_1)

Canonical Melnikov theory for diffeomorphisms

are two-dimensional manifolds which intersect transversally at a point q. Then the intersection is locally a one-dimensional smooth arc