13 citations · 45 across the 7 of their papers we have counts for
4 papers · 1 filter
The Lorenz system as a gradient-like system
Jeremy P Parker
We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-like system, i.e. that all bounded trajectories approach stationary points and therefor…
Predicting chaotic statistics with unstable invariant tori
Jeremy P. Parker, Omid Ashtari, Tobias M. Schneider
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic…
Invariant tori in dissipative hyperchaos
Jeremy P Parker, Tobias M Schneider
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's c…
A study of the double pendulum using polynomial optimization
Jeremy P Parker, David Goluskin, Geoffrey M Vasil
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtain…