# Dr Colin Christopher

## Biography

School of Computing, Electronics and Mathematics

## Teaching

### Teaching interests

I current teach:

MATH053/056 - Mathematical Methods 2

MATH187/188/189/190 - Engineering Mathematics

## Research

### 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

## Publications

Key publications

Key publications are highlighted

Journals
Articles
Christopher C, Llibre J, Pantazi C & Walcher S 2019 'On planar polynomial vector fields with elementary first integrals' Journal of Differential Equations , DOI PEARL
Vasco-Olmo JM, Diaz FA, James MN, Christopher CJ & Patterson EA 2017 'Experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields' Frattura ed Integrità Strutturale 11, (41) 166-174 , DOI PEARL
Hussein WMA & Christopher C 2017 'A Geometric Investigation of the Invariant Algebraic Curves in Two Dimensional Lotka–Volterra Systems' Mathematics in Computer Science 11, (3-4) 269-283 , DOI
Vasco-Olmo JM, James MN, Christopher CJ, Patterson EA & Díaz FA 2016 'Assessment of crack tip plastic zone size and shape and its influence on crack tip shielding' Fatigue & Fracture of Engineering Materials & Structures 39, (8) 969-981 , DOI PEARL
Laboviciute G, Christopher CJ, James MN & Patterson EA 2015 'Growth of inclined fatigue cracks using the biaxial CJP model' Frattura ed Integrità Strutturale 9, (33) 167-173 , DOI
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
Christopher CJ, Laboviciute G, James MN & Patterson EA 2013 'Extension of the CJP model to mixed mode I and mode II' Frattura ed Integrità Strutturale 7, (25) 161-166 , 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 2013 'Local Crack Plasticity and its Influences on the Global Elastic Stress Field' International Journal of Fatigue 46, 4-15 , 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' International Journal of Fatigue 46, 4-15 , 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 & Mardešic P 2010 'The monodromy problem and the tangential center problem' Functional Analysis and Its Applications 44, (1) 22-35 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, (6) 1197-1226 , DOI
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, 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 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 1999 'Liouvillian first integrals of second order polynomial differential equations' Electronic Journal of Differential Equations 1999, 1-7
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 CENTER IN CERTAIN CUBIC SYSTEMS' BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 22, 5-12 Author Site , 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, Hussein WMA & Wang Z 2016 'On the Integrability of Lotka–Volterra Equations: An Update' Springer Proceedings in Mathematics & Statistics Springer International Publishing 79-89 , DOI
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, Díaz Garrido FA, Vasco-Olmo JM, Kakiuchi T & Patterson EA 2016 'Interpretation of Plasticity Effects Using the CJP Crack Tip Field Model' 117-124 , DOI PEARL
Aziz W & Christopher C 2014 'On the integrability of some three-dimensional Lotka-Volterra equations with rank-1 resonances' Universitat Autonoma de Barcelona 37-48 , DOI
Giné J, Christopher C, Prešern M, Romanovski VG & Shcheglova NL 2012 'The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System' Springer Berlin Heidelberg 129-142 , DOI
James MN, Christopher CJ, Lu Y, Tee KF & Patterson EA 2011 'Crack Tip Shielding from a Plastic 'Inclusion'' 1-8 , DOI
James MN, Lu Y, Christopher CJ & Patterson EA 2010 'Full-field Modelling of Crack Tip Shielding via the 'Plastic Inclusion' Concept' 1-+ , DOI
Christopher C, James MN, Tee KF & Patterson EA 2008 'Evaluation of crack tip shielding using a photoelastic model' 333-338
Tee KF, Christopher CJ, James MN & Patterson EA 2007 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' 199-+ , 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' ICM-10 199-204