Rotational invariant circles of area-preserving maps are an important and well-studied
example of KAM tori. John Greene conjectured that the locally most robust rotational circles …

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 …

We propose rotation inferred from the polar decomposition of the flow gradient as a
diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical …

In Hamiltonian systems, depending on the control parameter, orbits can stay for very long
times around islands, the so-called stickiness effect caused by a temporary trapping …

In a pair of linked articles (called Papers I and II, respectively), we apply the concept of
Lagrangian Coherent Structures (LCSs) borrowed from the study of dynamical systems to …

The predictability of an orbit is a key issue when a physical model has strong sensitivity to
the initial conditions and it is solved numerically. How close the computed chaotic orbits are …

We present a simple method to efficiently compute a lower limit of the topological entropy
and its spatial distribution for two-dimensional mappings. These mappings could represent …

Hamiltonian systems that are either open, leaking, or contain holes in the phase space
possess solutions that eventually escape the system's domain. The motion described by …

A novel method is presented to calculate the sensitivity gradients of the largest Lyapunov
exponent (LLE) in dynamical systems. After the elimination of the discontinuity of state …

One of the main consequences of the complex hierarchical structure of chaotic regions and
stability islands in the phase space of a typical nonlinear Hamiltonian system is the …