The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation
properties quite distinct from those appearing in continuous nonlinear systems. For a large …

In this paper, we develop numerical methods based on the weighted Birkhoff average for
studying two-dimensional invariant tori for volume-preserving maps. The methods do not …

Invariant circles play an important role as barriers to transport in the dynamics of area-
preserving maps. KAM theory guarantees the persistence of some circles for near-integrable …

We previously showed that three-dimensional quadratic diffeomorphisms have anti-
integrable (AI) limits that correspond to a quadratic correspondence, a pair of one …

We study the spatial properties of a nonlinear discrete Schrödinger equation introduced by
Cai, Bishop, and Gro/nbech-Jensen [Phys. Rev. Lett. 72, 591 (1994)] that interpolates …

We compute all the cantori and their gap and turnstile structures, for area-preserving twist
maps near non-degenerate anti-integrable limits with arbitrarily many wells per period. The …

We use a modification of the parameterization method to study invariant manifolds for
difference equations. We establish existence, regularity, and smooth dependence on …

We study a two-parameter family of standard maps: the so-called two-harmonic family. In
particular, we study the areas of lobes formed by the stable and unstable manifolds …

Isochronous islands in phase space emerge in twist Hamiltonian systems as a response to
multiple resonant perturbations. According to the Poincaré-Birkhoff theorem, the number of …

For twist maps of the annulus and Tonelli Hamiltonians, two linear bundles, the Green
bundles, are defined along the minimizing orbits. The link between these Green bundles …