- Room 9 , 2 Kirkby Place, Drake Circus, Plymouth, PL4 8AA
- +44 1752 586857
- C.Christopher@plymouth.ac.uk
Profiles
Dr Colin Christopher
Associate Head of School
School of Engineering, Computing and Mathematics (Faculty of Science and Engineering)
Associate Head of School (Mathematics)
School of Computing, Electronics and Mathematics
Teaching interests
I current teach:
MATH053/056 - Mathematical Methods 2
MATH187/188/189/190 - Engineering Mathematics
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
Key publications are highlighted
Journals
Articles
2019 'On planar polynomial vector fields with elementary first integrals' Journal of Differential Equations , DOI Open access
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 Open access
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
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 Open access
2015 'Growth of inclined fatigue cracks using the biaxial CJP model' Frattura ed Integrità Strutturale 9, (33) 167-173 , DOI
2014 'On the trigonometric moment problem' Ergodic Theory and Dynamical Systems 34 Issue 01, 1-20 Publisher Site , DOI
2013 'Crack path support for deformation mechanisms in fatigue of polycarbonate' ENGINEERING FRACTURE MECHANICS 108, 89-97 , DOI
2013 'Extension of the CJP model to mixed mode I and mode II' Frattura ed Integrità Strutturale 7, (25) 161-166 , DOI
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
2013 'Local Crack Plasticity and its Influences on the Global Elastic Stress Field' International Journal of Fatigue 46, 4-15 , DOI
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
2012 'Fatigue crack growth and craze-induced crack tip shielding in polycarbonate' POLYMER 53, (7) 1558-1570 , DOI
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
2012 'Local integrability and linearizability of three-dimensional Lotka–Volterra systems' Applied Mathematics and Computation 219, 4067-4081 Publisher Site , DOI
2011 'Darboux integrating factors: inverse problems' Journal of Differential Equations 250, (1) 1-25 Publisher Site , DOI
2010 'The monodromy problem and the tangential center problem' Functional Analysis and Its Applications 44, (1) 22-35 Publisher Site , DOI
2010 'The monodromy problem and the tangential focus problem' Functional Analysis and Its Applications 44, (1) 22-35 Publisher Site , DOI
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
2008 'A quantitative evaluation of fatigue crack shielding forces using photoelasticity' ENGINEERING FRACTURE MECHANICS 75, (14) 4190-4199 , DOI
2008 'A quantitative evaluation of fatigue crack shielding forces using photoelasticity' ENGINEERING FRACTURE MECHANICS 75, (14) 4190-4199 , DOI
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
2007 'Inverse problems for multiple invariant curves' Proceedings of the Royal Society of Edinburgh Section A: Mathematics 137, (6) 1197-1226 , DOI
2007 'Towards a new model of crack tip stress fields' INTERNATIONAL JOURNAL OF FRACTURE 148, (4) 361-371 , DOI
2007 'Inverse problems for multiple invariant curves' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 137, 1197-1226 Publisher Site , DOI
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
2007 'Multiplicity of invariant algebraic curves in polynomial vector fields' Pacific Journal of Mathematics 229, 63-117 Publisher Site , DOI
2007 'The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point' Comptes Rendus Mathematique 345, (12) 695-698
2007 'Towards a new model of crack tip stress fields' International Journal of Fracture 148, (4) 361-371
2005 'Invariant algebraic curves of large degree for quadratic system' Journal of Mathematical Analysis and Applications 303, 450-461 Publisher Site , DOI
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
2004 'Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system' Qualitative Theory of Dynamical Systems 5, 11-61 Publisher Site , DOI
2004 'On the classification of Liénard systems with amplitude-independent periods' Journal of Differential Equations 200, 1-17 Publisher Site , DOI
2003 'Linearizability of three families of cubic systems' Journal of Physics. A. Mathematical and General 36, L145-L152 Publisher Site , DOI
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
2003 'The classical theory of invariants and object recognition using algebraic curves and surfaces' Journal of Mathematical Imaging and Vision 19, 237-253
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
2002 'Darboux integrability and invariant algebraic curves for planar polynomial systems' Journal of Physics. A. Mathematical and General 35, 2457-2476 Publisher Site , DOI
2001 'A note on the existence and global stability of deformations of compressible nonlinearly elastic solids' Archives of Mechanics 53, 195-204
2001 'Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in C-2' Publicacions Matematiques 45, (1) 95-123
2001 'Polynomial vector fields with prescribed algebraic limit cycles' Geometriae Dedicata 88, 255-258 Publisher Site , DOI
2000 'Abel equations: composition conjectures and the model problem' The Bulletin of the London Mathematical Society 32, 332-338 Publisher Site , DOI
2000 'Integrability via invariant algebraic curves for planar polynomial differential systems' Annals of Differential Equations. Weifen Fangcheng Niankan 16, 5-19
1999 'Liouvillian first integrals of second order polynomial differential equations' Electronic Journal of Differential Equations 1999, 1-7
1999 'Algebraic aspects of integrability for polynomial systems' Qualitative Theory of Dynamical Systems 1, 71-95 Publisher Site , DOI
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
1999 'Limit cycles in highly non-linear differential equations' Journal of Sound and Vibration 224, 505-517 Publisher Site , DOI
1999 'Liouvillian first integrals of second order polynomial differential equations' Electronic Journal of Differential Equations No. 49-7 pp. (electronic)
1999 'Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces' Nonlinearity 12, 1099-1112 Publisher Site , DOI
1998 'On the straightening of compressible, nonlinearly elastic, annular cylindrical sectors' Mathematics and Mechanics of Solids 3, 131-145 Publisher Site , DOI
1997 'Isochronous centers in planar polynomial systems' SIAM Journal on Mathematical Analysis 28, 162-177 Publisher Site , DOI
1997 'Quadratic-like cubic systems' Differential Equations and Dynamical Systems. An International Journal for Theory, Applications, and Computer Simulations 5, 329-345
1996 'Algorithmic derivation of centre conditions' SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 38, 619-636 Publisher Site , DOI
1996 'Small-amplitude limit cycles in polynomial Liénard systems' NoDEA. Nonlinear Differential Equations and Applications 3, 183-190 Publisher Site , DOI
1995 'On Cherkas’s method for centre conditions' Nonlinear World 2, 459-469
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
1994 'Invariant algebraic curves and conditions for a centre' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 124, 1209-1229
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
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
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 , DOI
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
1989 'Quadratic systems having a parabola as an integral curve' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 112, 113-134
Books
2007 Limit cycles of differential equations. Basel Birkhäuser Verlag Advanced Courses in Mathematics. CRM Barcelona
Chapters
2016 'On the Integrability of Lotka–Volterra Equations: An Update' Springer Proceedings in Mathematics & Statistics Springer International Publishing 79-89 , DOI
2005 'Estimating limit cycle bifurcations from centers' Differential equations with symbolic computation Basel Birkhäuser 23-35 Publisher Site , DOI
Conference Papers
2016 'Interpretation of Plasticity Effects Using the CJP Crack Tip Field Model' 117-124 , DOI Open access
2014 'On the integrability of some three-dimensional Lotka-Volterra equations with rank-1 resonances' Universitat Autonoma de Barcelona 37-48 , DOI
2012 'The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System' Springer Berlin Heidelberg 129-142 , DOI
2008 'Evaluation of crack tip shielding using a photoelastic model' 333-338
2007 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' 199-+ , DOI
2007 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' ICM-10 199-204