The Legendre transformation
The magnetic geodesic flow in a homogeneous field on the complex projective space.
The -centre problem of celestial mechanics for large energies
We consider the classical three-dimensional motion in a potential which is the sum of attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the centres, we find a universal behaviour for all energies above a positive threshold. Whereas for there are no bounded orbits, and for there is just one closed orbit, for the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....
The obstacle problem and direct products of unfurled swallowtails
The “octoid” with triple planar symmetry and its point orbits. (Das dreifach plansymmetrische "Oktoid" und seine Punktbahnen.)
The orbits about an oblate spheroid
The origin of variational principles
The Problem of Invariance for Covariant hamiltonians
The Problem of the Circular Billiard.
The quantum stability problem for time-periodic perturbations of the harmonic oscillator
The reduction of symplectic structure and Sternberg construction
The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
The Riemann tensor for nonholonomic manifolds.
The Rigid Body Dynamics: Classical and Algebro-geometric Integration
The rigid body with two controls and the Brockett perturbation.
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The single screw reciprocal to the general plane-symmetric six-screw linkage.
The spectral stability of the rigid body with three linear controls.