Dr R (Rory) Biggs

Tel: +27 12 420-3558
E-mail: [email protected]
Office: Mathematics building 2-25
Position: Senior Lecturer
Academic qualifications: MSc, PhD (Rhodes University)

Personal page: http://rorybiggs.weebly.com
OrcID: http://orcid.org/0000-0002-6388-7839
ResearchGate: https://www.researchgate.net/profile/Rory_Biggs

Fields of interest: Geometry, Topology, Algebra

Research interests: Differential geometry (and particularly sub-Riemannian geometry), geometric control theory, Lie groups and Lie algebras, Symplectic and Poisson geometry.

NRF rating: Y2      

Publications over the past five years

Journal articles

R Biggs, CC Remsing, A note on the equivalence of control systems on Lie groups. Bul. Acad. Stiinte Repub. Mold. Mat. 85(3)(2017) 63-73

R Biggs, CC Remsing, Invariant control systems on Lie groups: a short survey.  Extracta Math. 32(2)(2017), 213–238

DI Barrett, R Biggs, CC Remsing, Quadratic Hamilton–Poisson systems on se(1,1)*: the inhomogeneous case. Acta Appl. Math. 154(2018), 189–230.  

R Biggs. Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups. Commun. Math. 25(2017) 99–135

CE Bartlett, R Biggs, CC Remsing. Control systems on nilpotent Lie groups of dimension ≤ 4: equivalence and classification. Differential Geom. Appl. 54(2017),   282-297

R Biggs, G Falcone. A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms. Differential Geom. Appl. 54(2017), 251-263

R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems in three dimensions: equivalence, stability, and integration. Acta Appl. Math. 148(2017), 1-59.

​CE Bartlett, R Biggs, CC Remsing, A few remarks on quadratic Hamilton-Poisson systems on the Heisenberg Lie-Poisson space. Acta Math. Univ. Comenianae 86(1)(2017), 73-79.

RM Adams, R Biggs, W Holderbaum, CC Remsing, Stability and integration of Hamilton-Poisson systems on so(3)*. Rend. Mat. Appl., 37(2016), 1-42

R Biggs, CC Remsing, Equivalence of control systems on the pseudo-orthogonal group SO(2,1). An. Stiint. Univ. Ovidius Constanta. 24(2)(2016), 45-65.

DI Barrett, R Biggs, CC Remsing, O. Rossi, Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. J. Geom. Mech. 8(2)(2016), 139-167.

R Biggs, PT Nagy, Riemannian and sub-Riemannian structures on the Heisenberg groups. J. Dyn. Control Syst. 22(2016), 563-594.

R Biggs, CC Remsing, On the classification of real four-dimensional Lie groups. J. Lie Theory. 26(2016), 1001-1035.

R Biggs, PT Nagy, On extensions of sub-Riemannian structures on Lie groups. Differential Geom. Appl. 46(2016), 25-38.

CE Bartlett, R Biggs, CC Remsing, Control systems on the Heisenberg group: equivalence and classification. Publ. Math. Debrecen 88(1-2)(2016), 217-234.

DI Barrett, R Biggs, CC Remsing, Affine distributions on a four-dimensional extension of the semi-Euclidean group. Note Mat. 35(2)(2015), 81-97.

R Biggs, CC Remsing, On the equivalence of control systems on Lie groups. Commun. Math. 23(2)(2015), 119-129.

R Biggs, CC Remsing, Subspaces of the real four-dimensional Lie algebras: a classification of subalgebras, ideals, and full-rank subspaces. Extracta Math. 31(1)(2015), 41-93.

DI Barrett, R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems on se(1,1)*: the homogeneous case. Int. J. Geom. Methods Mod. Phys. 12(2015), 1550011 (17 pages).

R Biggs, CC Remsing, Some remarks on the oscillator group. Differential Geom. Appl. 35(2014), 199-209.

R Biggs, CC Remsing, Control systems on three-dimensional Lie groups: equivalence and controllability. J. Dyn. Control Syst. 20(3)(2014), 307-339.

DI Barrett, R Biggs, CC Remsing, Affine subspaces of the Lie algebra se(1,1). Eur. J. Pure Appl. Math. 7(2)(2014), 140-155.

R Biggs, CC Remsing, Cost-extended control systems on Lie groups. Mediterr. J. Math. 11(1)(2014), 193-215.

R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, II. Note Mat. 33(2)(2013), 19-31.

RM Adams, R Biggs, CC Remsing, Control systems on the orthogonal group SO(4). Commun. Math. 21(2)(2013), 107-128.

R Biggs, PT Nagy, A classification of sub-Riemannian structures on the Heisenberg groups. Acta Polytech. Hungar. 10(7)(2013), 41-52.

R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, I. Arch. Math. (Brno) 49(3)(2013), 187-197.

RM Adams, R Biggs, CC Remsing, Two-input control systems on the Euclidean group SE(2). ESAIM: Control Optim. Calc. Var. 19(4)(2013), 947-975.

R Biggs, CC Remsing, Control affine systems on semisimple three-dimensional Lie groups. An. Stiint. Univ. "A.I. Cuza" Iasi Mat. 59(2)(2013), 399-414.

RM Adams, R Biggs, CC Remsing, On some quadratic Hamilton-Poisson systems. Appl. Sci. 15(2013), 1-12.

R Biggs, CC Remsing, A note on the affine subspaces of three-dimensional Lie algebras. Bul. Acad. Stiinte Repub. Mold. Mat. 2012, no.3, 45-52.

RM Adams, R Biggs, CC Remsing, Equivalence of control systems on the Euclidean group SE(2). Control Cybernet. 41(3)(2012), 513-524.

R Biggs, CC Remsing, A category of control systems. An. St. Univ. Ovidius Constanta 20(1)(2012), 355-368.

RM Adams, R Biggs, CC Remsing, Single-input control systems on the Euclidean group SE(2). Eur. J. Pure Appl. Math. 5(1)(2012), 1-45.

 

Chapters in books

R Biggs, CC Remsing, Invariant control systems on Lie groups. In: G. Falcone (ed.), Lie Groups, Differential Equations, and Geometry, Springer, Cham, pp.127-181. DOI: 10.1007/978-3-319-62181-4_7; IN: ISBN: 978-3-319-62180-7 (Print) 978-3-319-62181-4 (Online); https://link.springer.com/book/10.1007/978-3-319-62181-4UNIPA Springer; Series info: https://www.springer.com/series/13175

Conference Proceedings

DI Barrett, R Biggs, CC Remsing, Optimal control of drift-free invariant control systems on the group of motions of the Minkowski plane. Proc. 13th European Control Conference, Strasbourg, France, 2014, pp 2466-2471. doi:10.1109/ECC.2014.6862313

R Biggs, CC Remsing, Control systems on three-dimensional Lie groups. Proc. 13th European Control Conference, Strasbourg, France, 2014,  2442-2447.  doi:10.1109/ECC.2014.6862312

RM Adams, R Biggs, CC Remsing, Quadratic Hamilton-Poisson systems on so(3)*: classification and integration. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 2013, pp 55-66. doi:10.7546/giq-15-2014-55-66

R Biggs, CC Remsing, A classification of quadratic Hamilton-Poisson systems in three dimensions. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 2013, pp 67-78. doi:10.7546/giq-15-2014-67-78

R Biggs, CC Remsing, Feedback classification of invariant control systems on three-dimensional Lie groups. Proc. 9th IFAC Symp. Nonlinear Control Syst., Toulouse, France, 2013, pp 506-511. doi:10.3182/20130904-3-fr-2041.00015

R Biggs, CC Remsing, On the equivalence of cost-extended control systems on Lie groups. Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal, 2012, pp 60-65. ISBN:978-1-61804-103-6

RM Adams, R Biggs, CC Remsing, On the equivalence of control systems on the orthogonal group SO(4). Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal, 2012, pp 54-59. ISBN:978-1-61804-103-6

 

Published by Annel Smit

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