Dr Colin Christopher
Profiles

Dr Colin Christopher

Associate Professor (Senior Lecturer) in Mathematics

School of Computing, Electronics and Mathematics (Faculty of Science and Engineering)

Role

Assistant Programme Manager for BSc Mathematics programmes

Teaching interests

I current teach:

MATH053 - Mathematical Methods 2

MATH054 - Mathematics for Computing

MATH055/056 - Mathematics 1 and 2

MATH2606 - Real and Complex Analysis

Research interests

Algebraic and analytic aspects of dynamical systems


especially:
  • Local and global integrability of vector fields
     
  • Algebraic aspects of integrability
  • Topics around Hilbert's 16th Problem
  • Application of monodromy techniques
  • Holomorphic dynamics

Key publications are highlighted

Journals
Articles
ÁLVAREZ AMELIA, BRAVO JLUIS & CHRISTOPHER COLIN 2014 'On the trigonometric moment problem' Ergodic Theory and Dynamical Systems 34 Issue 01, 1-20 Publisher Site , DOI
James MN, Lu Y, Christopher CJ & Patterson EA 2013 'Crack path support for deformation mechanisms in fatigue of polycarbonate' ENGINEERING FRACTURE MECHANICS 108, 89-97 Author Site , DOI
James MN, Christopher CJ, Lu Y & Patterson EA 2013 'Local Crack Plasticity and its Influences on the Global Elastic Stress Field' International Journal of Fatigue 46, 4-15 , DOI
Christopher C & Rousseau C 2013 'The Moduli Space of Germs of Generic Families of Analytic Diffeomorphisms Unfolding a Parabolic Fixed Point' International Mathematics Research Notices 2013, Publisher Site , DOI
James MN, Christopher CJ, Lu Y & Patterson EA 2012 'Fatigue crack growth and craze-induced crack tip shielding in polycarbonate' POLYMER 53, (7) 1558-1570 Author Site , DOI
Christopher C, Llibre J, Pantazi C & Walcher S 2012 'Inverse problems in Darboux’ theory of integrability' Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications 120, 101-126 Publisher Site , DOI
Aziz W & Christopher C 2012 'Local integrability and linearizability of three-dimensional Lotka–Volterra systems' Applied Mathematics and Computation 219, 4067-4081 Publisher Site , DOI
Christopher C, Llibre J, Pantazi C & Walcher S 2011 'Darboux integrating factors: inverse problems' Journal of Differential Equations 250, (1) 1-25 Publisher Site , DOI
Christopher C & Mardesic P 2010 'The monodromy problem and the tangential focus problem' Functional Analysis and Its Applications 44, (1) 22-35 Publisher Site , DOI
Christopher C, Llibre J, Pantazi C & Walcher S 2009 'Inverse problems for invariant algebraic curves: explicit computations' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 139, 287-302 Publisher Site , DOI
Christopher CJ, James MN, Patterson EA & Tee KF 2008 'A quantitative evaluation of fatigue crack shielding forces using photoelasticity' ENGINEERING FRACTURE MECHANICS 75, (14) 4190-4199 Author Site , DOI
Christopher CJ, James MN, Patterson EA & Tee KF 2008 'A quantitative evaluation of fatigue crack shielding forces using photoelasticity' ENGINEERING FRACTURE MECHANICS 75, (14) 4190-4199 Author Site , DOI
Christopher C & Schlomiuk D 2008 'On general algebraic mechanisms for producing centers in polynomial differential systems' Journal of Fixed Point Theory and Applications 3, 331-351 Publisher Site , DOI
Christopher C, Llibre J, Pantazi C & Walcher S 2007 'Inverse problems for multiple invariant curves' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 137, 1197-1226 Publisher Site , DOI
Rousseau C & Christopher C 2007 'Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle' Université de Grenoble. Annales de l’Institut Fourier 57, 301-360 Publisher Site
Christopher C, Llibre J & Pereira JV 2007 'Multiplicity of invariant algebraic curves in polynomial vector fields' Pacific Journal of Mathematics 229, 63-117 Publisher Site , DOI
Christopher C & Rousseau C 2007 'The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point' Comptes Rendus Mathematique 345, (12) 695-698
Christopher CJ, James MN, Patterson EA & Tee KF 2007 'Towards a new model of crack tip stress fields' International Journal of Fracture 148, (4) 361-371
Christopher CJ, James MN, Patterson EA & Tee KF 2007 'Towards a new model of crack tip stress fields' INTERNATIONAL JOURNAL OF FRACTURE 148, (4) 361-371 Author Site , DOI
Christopher C, Llibre J & Swirszcz G 2005 'Invariant algebraic curves of large degree for quadratic system' Journal of Mathematical Analysis and Applications 303, 450-461 Publisher Site , DOI
Christopher C, Mardešic P & Rousseau C 2004 'Normalizability, synchronicity, and relative exactness for vector fields in $\Bbb C^2$' Journal of Dynamical and Control Systems 10, 501-525 Publisher Site , DOI
Christopher C & Rousseau C 2004 'Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system' Qualitative Theory of Dynamical Systems 5, 11-61 Publisher Site , DOI
Christopher C & Devlin J 2004 'On the classification of Liénard systems with amplitude-independent periods' Journal of Differential Equations 200, 1-17 Publisher Site , DOI
Romanovski VG, Wu YH & Christopher C 2003 'Linearizability of three families of cubic systems' Journal of Physics. A. Mathematical and General 36, L145-L152 Publisher Site , DOI
Christopher C, Mardešic P & Rousseau C 2003 'Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $\Bbb C^2$' Journal of Dynamical and Control Systems 9, 311-363 Publisher Site , DOI
Çivi H, Christopher C & Erçil A 2003 'The classical theory of invariants and object recognition using algebraic curves and surfaces' Journal of Mathematical Imaging and Vision 19, 237-253
Christopher C & Llibre J 2002 'A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals' Proceedings of the American Mathematical Society 130, 2025-2030 (electronic) Publisher Site , DOI
Christopher C, Llibre J, Pantazi C & Zhang X 2002 'Darboux integrability and invariant algebraic curves for planar polynomial systems' Journal of Physics. A. Mathematical and General 35, 2457-2476 Publisher Site , DOI
Aron M & Christopher C 2001 'A note on the existence and global stability of deformations of compressible nonlinearly elastic solids' Archives of Mechanics 53, 195-204
Christopher C & Rousseau C 2001 'Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in C-2' Publicacions Matematiques 45, (1) 95-123
Christopher C 2001 'Polynomial vector fields with prescribed algebraic limit cycles' Geometriae Dedicata 88, 255-258 Publisher Site , DOI
Christopher C 2000 'Abel equations: composition conjectures and the model problem' The Bulletin of the London Mathematical Society 32, 332-338 Publisher Site , DOI
Christopher C & Llibre J 2000 'Integrability via invariant algebraic curves for planar polynomial differential systems' Annals of Differential Equations. Weifen Fangcheng Niankan 16, 5-19
Christopher C & Llibre J 1999 'Algebraic aspects of integrability for polynomial systems' Qualitative Theory of Dynamical Systems 1, 71-95 Publisher Site , DOI
Christopher C 1999 'An algebraic approach to the classification of centers in polynomial Liénard systems' Journal of Mathematical Analysis and Applications 229, 319-329 Publisher Site , DOI
Lynch S & Christopher CJ 1999 'Limit cycles in highly non-linear differential equations' Journal of Sound and Vibration 224, 505-517 Publisher Site , DOI
Christopher C 1999 'Liouvillian first integrals of second order polynomial differential equations' Electronic Journal of Differential Equations No. 49-7 pp. (electronic)
Christopher C & Lynch S 1999 'Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces' Nonlinearity 12, 1099-1112 Publisher Site , DOI
Aron M, Christopher C & Wang Y 1998 'On the straightening of compressible, nonlinearly elastic, annular cylindrical sectors' Mathematics and Mechanics of Solids 3, 131-145 Publisher Site , DOI
Christopher CJ & Devlin J 1997 'Isochronous centers in planar polynomial systems' SIAM Journal on Mathematical Analysis 28, 162-177 Publisher Site , DOI
Lloyd NG, Christopher CJ, Devlin J, Pearson JM & Yasmin N 1997 'Quadratic-like cubic systems' Differential Equations and Dynamical Systems. An International Journal for Theory, Applications, and Computer Simulations 5, 329-345
Pearson JM, Lloyd NG & Christopher CJ 1996 'Algorithmic derivation of centre conditions' SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 38, 619-636 Publisher Site , DOI
Christopher CJ & Lloyd NG 1996 'Small-amplitude limit cycles in polynomial Liénard systems' NoDEA. Nonlinear Differential Equations and Applications 3, 183-190 Publisher Site , DOI
Christopher CJ, Lloyd NG & Pearson JM 1995 'On Cherkas’s method for centre conditions' Nonlinear World 2, 459-469
Christopher CJ & Lloyd NG 1995 'Polynomial systems: a lower bound for the Hilbert numbers' Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences 450, 219-224 Publisher Site , DOI
Christopher CJ 1994 'Invariant algebraic curves and conditions for a centre' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 124, 1209-1229
Christopher C & Devlin J 1993 'A note on the replicator equations of dynamical game theory' Applied Mathematics Letters. An International Journal of Rapid Publication 6, 31-33 Publisher Site , DOI
Kooij RE & Christopher CJ 1993 'Algebraic invariant curves and the integrability of polynomial systems' Applied Mathematics Letters. An International Journal of Rapid Publication 6, 51-53 Publisher Site , DOI
Christopher CJ & Lloyd NG 1990 'On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems' Bulletin of the London Mathematical Society 22, (1) 5-12 , DOI
Christopher CJ & Lloyd NG 1990 'On the paper of X. Jin and D. Wang concerning the conditions for a centre in certain cubic systems: “On the conditions of Kukles for the existence of a centre” [Bull. London Math. Soc. \bf 22 (1990), no. 1, 1–4; MR1026764 (90m:34071)]' The Bulletin of the London Mathematical Society 22, 5-12 Publisher Site , DOI
Christopher C 1989 'Quadratic systems having a parabola as an integral curve' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 112, 113-134
Books
Christopher C & Li C 2007 Limit cycles of differential equations. Basel Birkhäuser Verlag Advanced Courses in Mathematics. CRM Barcelona
Chapters
Christopher C 2005 'Estimating limit cycle bifurcations from centers' Differential equations with symbolic computation Basel Birkhäuser 23-35 Publisher Site , DOI
Conference Papers
James MN, Christopher CJ, Lu Y, Tee KF & Patterson EA 2011 'Crack Tip Shielding from a Plastic 'Inclusion'' //0 //0 1-8 , DOI
James MN, Lu Y, Christopher CJ & Patterson EA 2010 'Full-field Modelling of Crack Tip Shielding via the 'Plastic Inclusion' Concept' //0 //0 1-+ , DOI
Tee KF, Christopher CJ, James MN & Patterson EA 2007 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' //0 //0 199-+
Tee KF, Christopher CJ, James MN & Patterson EA 2007 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' ICM-10 //0 //0 199-204