Normal forms approach to diffusion near hyperbolic equilibria

On hyperbolic normal forms of robot kinematics

We study redundant robot kinematics around singular configurations of corank 1. Sufficient conditions are derived under which the kinematics become equivalent to a hyperbolic normal form. These conditions are specified further to non-redundant kinematics, and illustrated with examples of a double pendulum with links of equal length at the fully folded down configuration as well as of the PUMA m...

Normal Forms, Resonances, and Meandering Tip Motions near Relative Equilibria of Euclidean Group Actions

The equivariant dynamics near relative equilibria to actions of noncompact, nite-dimensional Lie groups G can be described by a skew product ow on a center manifold: _ g = ga(v); _ v = '(v) with g 2 G, with v in a slice transverse to the group action, and a(v) in the Lie algebra of G: We present a normal form theory near relative equilibria '(v=0) = 0; in this general case. For the speci c case...

A Spectral Sequence Approach to Normal Forms

Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria

We discuss dynamics near homoclinic orbits to saddle-focus equilibria in threedimensional vector fields. The existence of periodic and strange attractors is investigated not in unfoldings, but in families for which each member has a homoclinic orbit. We consider how often, in the sense of measure, periodic and strange attractors occur in such families. We also discuss the fate of typical orbits...

Near Optimal Algorithms for Computing Smith Normal Forms of Integer

We present new algorithms for computing Smith normal forms of matrices over the integers and over the integers modulo d. For the case of matrices over Z Z d, we present an algorithm that computes the Smith form S of an A 2 Z Z nm d in only O(n ?1 m) operations from Z Z d. Here, is the exponent for matrix multiplication over rings: two n n matrices over a ring R can be multiplied in O(n) operati...