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This is a bunch of unpublished stuff.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)