Andrew D. Lewis's Notes
This is a bunch of unpublished stuff. Some of it I was not
able to get published (sometimes for good reasons, sometimes
for not good reasons), some are notes from seminars, and
some are just random things I wrote.
The listing is roughly in reverse chronological order.
The "Last Updated" tag means the last time the
postscript files were updated, not the TeX files.
- 2024a
- Title: Chaotic dynamics in deterministic dynamical systems
Author(s): Andrew D. Lewis
Detail: Preprint for a handbook of nonlinear dynamics
- 2020a
- Title: Geometric analysis on real analytic manifolds
Author(s): Andrew D. Lewis
Detail: Preliminary musings that turned into my book in Springer's Lecture
Notes in Mathematics with the same name
- 2014a
- Title: Local reachability of control systems in étalé Lie
groupoids
Author(s): Saber Jafarpour and Andrew D. Lewis
Detail: Miscellaneous
- 2013a
- Title: A canonical treatment of line bundles over general projective spaces
Detail: Random notes
(arXiv:2309.11121)
- 2011a
- Title: Generalised subbundles, distributions, and families of vector fields:
A comprehensive review
Author(s): Andrew D. Lewis
Detail: Part of notes prepared for a 2012 Summer School at ICMAT in Madrid
(arXiv:2309.10471)
- 2010a
- Title: A top nine list: Most popular induced matrix norms
Author(s): Andrew D. Lewis
Detail: Miscellaneous
(arXiv:2309.07190)
- 2009c
- Title: Subsets of Euclidean domains possessing a unique division
algorithm
Author(s): Andrew D. Lewis
Detail: Miscellaneous
- 2009b
- Title: A square Riemann integrable function whose Fourier transform is not
square Riemann integrable
Author(s): Andrew D. Lewis
Detail: Miscellaneous
- 2009a
- Title: Semicontinuity of rank and nullity and some consequences
Detail: Random notes
- 2007c
- Title: Should we fly in the Lebesgue-designed airplane? - The correct defence
of the Lebesgue integral
Author(s): Andrew D. Lewis
Detail: Miscellaneous (arXiv:2309.08908)
- 2007b
- Title: Connections and spaces of connections
Detail: Seminar on Foundations of Differential Geometry, Summer 2007
- 2007a
- Title: An illustration of Wang's Theorem
Detail: Seminar on Foundations of Differential Geometry, Spring 2007
- 2006c
- Title: Frobenius's Theorem via Spencer theory
Detail: Notes from MATH 949
- 2006b
- Title: Geometric partial differential equations: Definitions and
properties
Detail: Notes from MATH 949
- 2006a
- Title: The bundle of infinite jets
Detail: Notes from MATH 949
- 2005c
- Title: The formal Poincaré Lemma
Detail: Notes from MATH 949
- 2005b
- Title: Some jet bundle structure
Detail: Notes from MATH 949
- 2005a
- Title: The affine structure of jet bundles
Detail: Notes from MATH 949
- 2002c
- Title: Geometric sliding mode control: The linear and linearised
theory
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: An unapplied approach to sliding mode control, so of interest to no one.
- 2002b
- Title: The linearisation of a simple mechanical control system
Author(s): Francesco Bullo and Andrew D. Lewis
Detail: Miscellaneous
- 2002a
- Title: Geometric local controllability: second-order conditions
Author(s): Ron M. Hirschorn and Andrew D. Lewis
Detail: This is a long paper detailing an approach to controllability that I
am no longer pursuing. Interesting stuff though.
- 2001a
- Title: A brief on controllability of nonlinear systems
Detail: Mathematics & Statistics Control Seminar, Queen's University,
Fall 2001
- 2000c
- Title: Optimal control for a simplified hovercraft model
Author(s): A. Theo Coombs and Andrew D. Lewis
Detail: Miscellaneous
- 2000b
- Title: The geometry of the maximum principle for affine connection control
systems
Author(s): Andrew D. Lewis
Detail: Now a part of the supplementary material in my book Geometric
Control of Mechanical Systems with Francesco Bullo
- 2000a
- Title: Momentum shift in cotangent bundle reduction
Detail: Research notes, Spring 2000
- 1998a
- Title: Lifting distributions to tangent and jet bundles
Author(s): Andrew D. Lewis
Detail: Miscellaneous
- 1997c
- Title: Variational principles for nonlinearly constrained systems in one
independent variable
Author(s): Andrew D. Lewis
Detail: Miscellaneous
- 1997b
- Title: Energy-preserving affine connections
Author(s): Andrew D. Lewis
Detail: Miscellaneous
- 1997a
- Title: Reduction of simple mechanical systems
Detail: Mechanics and symmetry seminars, University of Warwick,
Fall 1997
- 1995b
- Title: Some two-dimensional manifolds with affine connections
Detail: Geometry reading group, California Institute of Technology,
Fall 1995 - Winter 1996
- 1995a
- Title: Notes on linear frame bundles
Detail: Geometry reading group, California Institute of Technology,
Fall 1995 - Winter 1996
- 1993b
- Title: Notes on mechanics, symmetry, reduction, holonomy, and control
Detail: Mechanical systems reading group, California Institute of
Technology, Summer 1993
- 1993a
- Title: Notes on principal fibre bundles
Detail: Mechanical systems reading group, California Institute of
Technology, Summer 1993
- 1992a
- Title: Group structures in a class of control systems
Author(s): Andrew D. Lewis
Detail: Miscellaneous
Andrew D. Lewis (andrew at mast.queensu.ca)