4 citations · 16 across the 13 of their papers we have counts for
13 papers
The Fundamental Theorem of Dynamical Systems: all at once and all in the same place
Andrew D. Lewis
The so-called Fundamental Theorem of Dynamical Systems -- which(1) relates attractors and repellers to the chain recurrent set and (2) gives the existence of a complete Lyapunov fu…
Invariance of subbundles and nonholonomic trajectories
Andrew D. Lewis, Ahmed Gamal Shaltut
In the comparison of nonholonomic mechanics and constrained variational mechanics, invariant affine subbundles arise in the determination of the initial conditions where the two me…
Topologies for geometric flows and continuous dependence on parameters
Andrew D. Lewis, Yanlei Zhang
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are consi…
A canonical treatment of line bundles over general projective spaces
Andrew D. Lewis
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presente…
Generalised subbundles and distributions: A comprehensive review
Andrew D. Lewis
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geome…
Should we fly in the Lebesgue-designed airplane? -- The correct defence of the Lebesgue integral
Andrew D. Lewis
It is well-known that the Lebesgue integral generalises the Riemann integral. However, as is also well-known but less frequently well-explained, this generalisation alone is not th…