State transition matrix of variational integrators for Halo orbits

A Numerical Method for Computing the State Transition Matrix Using Poincaré Integral Invariants

Symplectic filtering of Hamiltonian dynamics with moving sensors

While structure-preserving methods for the forward simulation of Hamiltonian systems are well established, the mathematical foundations of their data assimilation and filtering counterparts remain comparatively less developed, particularly regarding rigorous accuracy guarantees. To address this gap, we propose an onlin...

Variational Structure at the Edge of Stability

When discrete-time optimizers operate at the edge of stability, they exhibit near-two-periodic behavior. These oscillatory dynamics are reminiscent of conservative systems, such as the dynamics generated by symplectic integrators. However, a precise formulation of the connection between discrete-time optimizers at the...

Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric $N$-Body Problems

Many mechanical systems, such as the Newtonian $n$-body system, are invariant under rotations. The rotational symmetry of the system gives rise to two commuting actions: the dynamical action and the action of the symmetry group. In this paper, we exploit this symmetry to construct families of periodic and quasi-periodi...

Some explorations of Kirchhoff dynamics

The classical problem of a rigid body in an ideal fluid is a six-dimensional dynamical system with three conserved quantities. Despite its long history and its importance as a reduced model of many fluid-structure problems, basic questions remain, including the shapes and connectivities of the three-dimensional submani...

From Transition-State Geometry to Gap Times: What Lagrangian Betweenness Measures in Chemical Reaction Dynamics

A chemical transition state is a phase-space bottleneck: trajectories approach along stable directions and leave along unstable directions. Lagrangian betweenness (LB), introduced in finite-time transport theory for fluid flows, combines backward and forward deformation in a way suggestive of this gather-and-disperse g...