We prove an analogue of Lang's conjecture on divisible groups for polynomial dynamical systems over number fields. In our setting, the role group is taken by small orbit a point $\alpha$ where $f$ given \begin{align*} \mathcal{S}_\alpha = \{\beta \in \mathbb{C}; f^{\circ n}(\beta) n}(\alpha) \text{ some } n \mathbb{Z}_{\geq 0}\}. \end{align*} Our main theorem classification algebraic relations ...

A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid-body and muscle dynamics described with a Hill-type driven by neural control inputs. objective to find input state trajectories that are optimal respect minimum-effort meet constraints associated models. measure effort given the integral pairwise average forces agonist-antagonist...

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the expansion coefficients. Here we study the structure and dynamics of these differential equations when the original system has Hamiltonian structure, has multiple t...

In optimal kinodynamic planning, given a robot system, we must nd a minimal-time trajectory that goes from a start state to a goal state while avoiding obstacles by a speed-dependent safety-margin and respecting dynamics bounds. With Canny and Reif 1], we approached this problem from an-approximation standpoint and introduced a provably-good approximation algorithm for optimal kinodynamic plann...

We consider polynomial maps of the form f(z,w) = (p(z), q(z,w)) that extend as holomorphic maps of CP. Mattias Jonsson introduces in “Dynamics of polynomial skew products on C2” [Math. Ann., 314(3): 403– 447, 1999] a notion of connectedness for such polynomial skew products that is analogous to connectivity for the Julia set of a polynomial map in one-variable. We prove the following dichotomy:...

We study a three-dimensional model for driven granular media in which particles interact inelastically while they follow Brownian dynamics in between collisions. A steady Boltzmann-type kinetic equation associated with a pseudo-Maxwellian model is analyzed. Homogeneous steady states are found by a small inelasticity expansion. These states are given by a Maxwellian distribution corrected by the...