- Room 9 , 2 Kirkby Place, Drake Circus, Plymouth, PL4 8AA
- +44 1752 586857
- C.Christopher@plymouth.ac.uk
Profiles
Dr Colin Christopher
Associate Professor in Mathematics
School of Engineering, Computing and Mathematics (Faculty of Science and Engineering)
Biography
Biography
- Associate Professor in Mathematics
- School of Computing, Electronics and Mathematics
Teaching
Teaching
Teaching interests
I current teach:
- MATH053 - Mathematical Methods 2
- MATH1610 - Probability with Applications
- MATH2606 - Real and Complex Analysis
Research
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
Publications
Key publications
Key publications are highlighted
Journals
Articles
(2021) 'Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture' Functional Analysis and Its Applications 55, (4) 257-271 , DOI
(2021) 'Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance' Mediterranean Journal of Mathematics 18, (4) , DOI
(2021) 'Analytic integrability of certain resonant saddle' Chaos, Solitons and Fractals 146, , DOI Open access
(2021) 'Инфинитезимальная проблема центра на нулевых циклах и гипотеза композиции' Функциональный анализ и его приложения 55, (4) 3-21 , DOI
(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
(2010) 'Проблема монодромии и инфинитезимальная проблема фокуса' Функциональный анализ и его приложения 44, (1) 27-43 , 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) 'Towards a new model of crack tip stress fields' International Journal of Fracture 148, (4) 361-371
(2007) 'The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point' Comptes Rendus Mathematique 345, (12) 695-698
(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) 'On the classification of Liénard systems with amplitude-independent periods' Journal of Differential Equations 200, 1-17 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
(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
Personal
Personal