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A Tour of Subriemannian Geometries, Their Geodesics and Applications
Geodesics in subriemannian manifolds: Dido meets Heisenberg Chow's theorem: Getting from A to B A remarkable horizontal curve Curvature and nilpotentization Singular curves and geodesics A zoo ofExpand
A remarkable periodic solution of the three-body problem in the case of equal masses
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetryExpand
Isoholonomic problems and some applications
We study the problem of finding the shortest loops with a given holonomy. We show that the solutions are the trajectories of particles in Yang-Mills potentials (Theorem 4), or, equivalently, theExpand
Hearing the zero locus of a magnetic field
AbstractWe investigate the ground state of a two-dimensional quantum particle in a magnetic field where the field vanishes nondegenerately along a closed curve. We show that the ground stateExpand
Embedding bounded degree spanning trees in random graphs
We prove that if a tree $T$ has $n$ vertices and maximum degree at most $\Delta$, then a copy of $T$ can almost surely be found in the random graph $\mathcal{G}(n,\Delta\log^5 n/n)$.
Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization
A nonholonomic system, for short “NH,” consists of a configuration space Q n, a Lagrangian \( L(q,\dot q,t) \), a nonintegrable constraint distribution \( \mathcal{H} \subset TQ \), with dynamicsExpand
Momentum maps and classical relativistic fields. Part 1: Covariant Field Theory
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connectionsExpand
Spanning trees in random graphs
For each $\Delta>0$, we prove that there exists some $C=C(\Delta)$ for which the binomial random graph $G(n,C\log n/n)$ almost surely contains a copy of every tree with $n$ vertices and maximumExpand
Infinitely Many Syzygies
Abstract We show that any bounded zero-angular-momentum solution of the Newtonian three-body problem suffers infinitely many syzygies (collinearities) provided that it does not suffer a tripleExpand
Abnormal Minimizers
This paper constructs the first example of a singular, abnormal minimizer for the Lagrange problem with linear velocity constraints and quadratic definite Lagrangian, or, equivalently, for an optimalExpand