Colin Christopher

Dr Colin Christopher

Job title: Associate Professor (Senior Lecturer) in Mathematics, School of Computing and Mathematics (Faculty of Science and Technology)
Address: Room 9 , 2 Kirkby Place, Drake Circus,
Plymouth, Devon, PL4 8AA
Telephone: +441752586857
Alternative telephone: +44 (0)1752 232720
Facsimile: +44 (0)1752 232780
Email: C.Christopher@plymouth.ac.uk

Role

Programme Manager for

Foundation Pathways in Technology

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 pp 23 - 35 http://dx.doi.org/10.1007/3-7643-7429-2_2 , DOI: 10.1007/3-7643-7429-2_2

Conference Papers

James, MN., Christopher, CJ., Lu, YW., Tee, KF. & Patterson, EA. (2011) 'Crack Tip Shielding from a Plastic 'Inclusion'' in Sandera P (ed.) 6th International Conference on Materials Structure and Micromechanics of Fracture. Brno, CZECH REPUBLIC 28/06/2010 - 30/06/2010 TRANS TECH PUBLICATIONS LTD pp 1 - 8 , DOI: 10.4028/www.scientific.net/KEM.465.1

James, MN., Lu, YW., Christopher, CJ. & Patterson, EA. (2010) 'Full-field Modelling of Crack Tip Shielding via the 'Plastic Inclusion' Concept' in Xie LY,James MN,Zhao YX,Qian WX (ed.) 2nd International Conference on Advances in Product Development and Reliability. Shenyang, PEOPLES R CHINA 28/07/2010 - 30/07/2010 TRANS TECH PUBLICATIONS LTD pp 1 - 9 , DOI: 10.4028/www.scientific.net/AMR.118-120.1

Tee, KF., Christopher, CJ., James, MN. & Patterson, EA. (2007) 'New insights into plasticity-induced crack tip shielding via mathematical modelling and full field photoelasticity' in Nam SW,Chang YW,Lee SB,Kim NJ (ed.) 10th International Conference on Mechanical Behavior of Materials. Busan, SOUTH KOREA 27/05/2007 - 31/05/2007 TRANS TECH PUBLICATIONS LTD pp 199 - 204

Journals

Articles

Christopher, C., Llibre, J., Pantazi, C. & Walcher, S. (2011) 'Darboux integrating factors: inverse problems' Journal of Differential Equations 250, pp 1 - 25 http://dx.doi.org/10.1016/j.jde.2010.10.013 , DOI: 10.1016/j.jde.2010.10.013

Christopher, C. & Mardešic, P. (2010) 'The monodromy problem and the tangential center problem' Functional Analysis and Its Applications 44, pp 22-35 - 22-35 http://dx.doi.org/10.1007/s10688-010-0003-4

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, pp 287 - 302 http://dx.doi.org/10.1017/S0308210507001175 , DOI: 10.1017/S0308210507001175

Christopher, CJ., James, MN., Patterson, EA. & Tee, KF. (2008) 'A quantitative evaluation of fatigue crack shielding forces using photoelasticity' ENG FRACT MECH 75 (14), pp 4190 - 4199 , DOI: 10.1016/j.engfracmech.2008.03.013

Christopher, C. & Schlomiuk, D. (2008) 'On general algebraic mechanisms for producing centers in polynomial differential systems' Journal of Fixed Point Theory and Applications 3, pp 331 - 351 http://dx.doi.org/10.1007/s11784-008-0077-2 , DOI: 10.1007/s11784-008-0077-2

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, pp 1197 - 1226 http://dx.doi.org/10.1017/S0308210506000400 , DOI: 10.1017/S0308210506000400

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, pp 301 - 360 http://aif.cedram.org/item?id=AIF_2007__57_1_301_0

Christopher, C., Llibre, J. & Pereira, JV. (2007) 'Multiplicity of invariant algebraic curves in polynomial vector fields' Pacific Journal of Mathematics 229, pp 63 - 117 http://dx.doi.org/10.2140/pjm.2007.229.63 , DOI: 10.2140/pjm.2007.229.63

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), pp 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), pp 361 - 371

Christopher, CJ., James, MN., Patterson, EA. & Tee, KF. (2007) 'Towards a new model of crack tip stress fields' INT J FRACTURE 148 (4), pp 361 - 371 , DOI: 10.1007/s10704-008-9209-3

Christopher, C., Llibre, J. & Swirszcz, G. (2005) 'Invariant algebraic curves of large degree for quadratic system' Journal of Mathematical Analysis and Applications 303, pp 450 - 461 http://dx.doi.org/10.1016/j.jmaa.2004.08.042 , DOI: 10.1016/j.jmaa.2004.08.042

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, pp 501 - 525 http://dx.doi.org/10.1023/B:JODS.0000045362.42314.60 , DOI: 10.1023/B:JODS.0000045362.42314.60

Christopher, C. & Rousseau, C. (2004) 'Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system' Qualitative Theory of Dynamical Systems 5, pp 11 - 61 http://dx.doi.org/10.1007/BF02968129 , DOI: 10.1007/BF02968129

Christopher, C. & Devlin, J. (2004) 'On the classification of Liénard systems with amplitude-independent periods' Journal of Differential Equations 200, pp 1 - 17 http://dx.doi.org/10.1016/j.jde.2004.01.008 , DOI: 10.1016/j.jde.2004.01.008

Romanovski, VG., Wu, YH. & Christopher, C. (2003) 'Linearizability of three families of cubic systems' Journal of Physics. A. Mathematical and General 36, pp L145 - L152 http://dx.doi.org/10.1088/0305-4470/36/9/101 , DOI: 10.1088/0305-4470/36/9/101

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, pp 311 - 363 http://dx.doi.org/10.1023/A:1024643521094 , DOI: 10.1023/A:1024643521094

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, pp 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, pp 2025 - 2030 (electronic) http://dx.doi.org/10.1090/S0002-9939-01-06253-0 , DOI: 10.1090/S0002-9939-01-06253-0

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, pp 2457 - 2476 http://dx.doi.org/10.1088/0305-4470/35/10/310 , DOI: 10.1088/0305-4470/35/10/310

Aron, M. & Christopher, C. (2001) 'A note on the existence and global stability of deformations of compressible nonlinearly elastic solids' Archives of Mechanics 53, pp 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), pp 95 - 123

Christopher, C. (2001) 'Polynomial vector fields with prescribed algebraic limit cycles' Geometriae Dedicata 88, pp 255 - 258 http://dx.doi.org/10.1023/A:1013171019668 , DOI: 10.1023/A:1013171019668

Christopher, C. (2000) 'Abel equations: composition conjectures and the model problem' The Bulletin of the London Mathematical Society 32, pp 332 - 338 http://dx.doi.org/10.1112/S0024609300006998 , DOI: 10.1112/S0024609300006998

Christopher, C. & Llibre, J. (2000) 'Integrability via invariant algebraic curves for planar polynomial differential systems' Annals of Differential Equations. Weifen Fangcheng Niankan 16, pp 5 - 19

Christopher, C. & Llibre, J. (1999) 'Algebraic aspects of integrability for polynomial systems' Qualitative Theory of Dynamical Systems 1, pp 71 - 95 http://dx.doi.org/10.1007/BF02969405 , DOI: 10.1007/BF02969405

Christopher, C. (1999) 'An algebraic approach to the classification of centers in polynomial Liénard systems' Journal of Mathematical Analysis and Applications 229, pp 319 - 329 http://dx.doi.org/10.1006/jmaa.1998.6175 , DOI: 10.1006/jmaa.1998.6175

Lynch, S. & Christopher, CJ. (1999) 'Limit cycles in highly non-linear differential equations' J SOUND VIB 224 (3), pp 505 - 517

Christopher, C. (1999) 'Liouvillian first integrals of second order polynomial differential equations' Electronic Journal of Differential Equations , pp 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, pp 1099 - 1112 http://dx.doi.org/10.1088/0951-7715/12/4/321 , DOI: 10.1088/0951-7715/12/4/321

Aron, M., Christopher, C. & Wang, Y. (1998) 'On the straightening of compressible, nonlinearly elastic, annular cylindrical sectors' Mathematics and Mechanics of Solids 3, pp 131 - 145 http://dx.doi.org/10.1177/108128659800300201 , DOI: 10.1177/108128659800300201

Christopher, CJ. & Devlin, J. (1997) 'Isochronous centers in planar polynomial systems' SIAM J MATH ANAL 28 (1), pp 162 - 177

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, pp 329 - 345

Pearson, JM., Lloyd, NG. & Christopher, CJ. (1996) 'Algorithmic derivation of centre conditions' SIAM REV 38 (4), pp 619 - 636

Christopher, CJ. & Lloyd, NG. (1996) 'Small-amplitude limit cycles in polynomial Liénard systems' NoDEA. Nonlinear Differential Equations and Applications 3, pp 183 - 190 http://dx.doi.org/10.1007/BF01195913 , DOI: 10.1007/BF01195913

Christopher, CJ., Lloyd, NG. & Pearson, JM. (1995) 'On Cherkas’s method for centre conditions' Nonlinear World 2, pp 459 - 469

CHRISTOPHER, CJ. & LLOYD, NG. (1995) 'POLYNOMIAL SYSTEMS - A LOWER-BOUND FOR THE HILBERT-NUMBERS' P ROY SOC LOND A MAT 450 (1938), pp 219 - 224

CHRISTOPHER, CJ. (1994) 'INVARIANT ALGEBRAIC-CURVES AND CONDITIONS FOR A CENTER' P ROY SOC EDINB A 124, pp 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, pp 31 - 33 http://dx.doi.org/10.1016/0893-9659(93)90119-8 , DOI: 10.1016/0893-9659(93)90119-8

KOOIJ, RE. & CHRISTOPHER, CJ. (1993) 'ALGEBRAIC INVARIANT CURVES AND THE INTEGRABILITY OF POLYNOMIAL SYSTEMS' APPL MATH LETT 6 (4), pp 51 - 53

CHRISTOPHER, CJ. & LLOYD, NG. (1990) 'ON THE PAPER OF JIN AND WANG CONCERNING THE CONDITIONS FOR A CENTER IN CERTAIN CUBIC SYSTEMS' B LOND MATH SOC 22, pp 5 - 12

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, pp 5 - 12 http://dx.doi.org/10.1112/blms/22.1.5 , DOI: 10.1112/blms/22.1.5

Christopher, C. (1989) 'Quadratic systems having a parabola as an integral curve' Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 112, pp 113 - 134

Links

School of Mathematics and Statistics