- Room 9 , 2 Kirkby Place, Drake Circus, Plymouth, Devon, PL4 8AA
- +44 1752 586857
- C.Christopher@plymouth.ac.uk
Profiles
Dr Colin Christopher
Associate Professor 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
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
2017
'Experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields'
Frattura ed Integrita Strutturale
11,
(41)
166-174
, DOI
PEARL
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
2015
'Growth of inclined fatigue cracks using the biaxial CJP model'
Frattura ed Integrita 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
'Extension of the CJP model to mixed mode I and mode II'
Frattura ed Integrita Strutturale
7,
(25)
161-166
, DOI
2013
'Crack path support for deformation mechanisms in fatigue of polycarbonate'
ENGINEERING FRACTURE MECHANICS
108,
89-97
, 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 Centre in certain Cubic Systems'
Bulletin of the London Mathematical Society
22,
(1)
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 and Statistics
79-89
, DOI
2005
'Estimating limit cycle bifurcations from centers'
Differential equations with symbolic computation
Basel
Birkhäuser
23-35
Publisher Site
, DOI
Conference Papers
2014
'On the integrability of some three-dimensional Lotka-Volterra equations with rank-1 resonances'
37-48
, DOI
2012
'The resonant center problem for a 2:-3 resonant cubic lotka–volterra system'
129-142
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