Publication list also available on ReseachGate and ORCID.

Book ​chapters

  • R Biggs, CC Remsing, Invariant control systems on Lie groups. In: G. Falcone (ed.), Lie Groups, Differential Equations, and Geometry: Advances and Surveys, Springer, Cham, 2017,  pp.127-181.  DOI | RG

Journal articles

2018

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

2017

  • R Biggs, Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups. Commun. Math. 25 (2017) 99–135. ​DOI | RG
  • R Biggs, G Falcone, A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms. Differential Geom. Appl. 54(2017), 251–263.  DOI | RG
  • 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.​ DOI | RG
  • R Biggs, CC Remsing, Quadratic Hamilton–Poisson systems in three dimensions: equivalence, stability, and integration. Acta Appl. Math. 148(2017), 1–59.  DOI | Online PDF | RG
  • ​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. Link | ​RG​
  • R Biggs, CC Remsing, Invariant control systems on Lie groups: a short survey.  Extracta Math. 32(2)(2017), 213–238.  Link | RG

2016

  • 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. DOI | RG
  • 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. DOI | RG
  • R Biggs, PT Nagy, On sub-Riemannian and Riemannian structures on the Heisenberg groups. J. Dyn. Control Syst. 22(2016), 563–594. DOI | RG
  • R Biggs, CC Remsing, On the classification of real four-dimensional Lie groups. J. Lie Theory. 26(2016), 1001–1035. Link | RG
  • R Biggs, PT Nagy, On extensions of sub-Riemannian structures on Lie groups. Differential Geom. Appl. 46(2016), 25–38. DOI | RG
  • CE Bartlett, R Biggs, CC Remsing, Control systems on the Heisenberg group: equivalence and classification. Publ. Math. Debrecen 88(1-2)(2016), 217–234. Link | RG​
  • 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. Link | RG​

2015

  • 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. DOI | RG
  • R Biggs, CC Remsing, On the equivalence of control systems on Lie groups. Commun. Math. 23(2)(2015), 119–129. Link | RG
  • 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. Link | RG
  • 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). DOI | ​RG

2014

  • R Biggs, CC Remsing, Some remarks on the oscillator group. Differential Geom. Appl. 35(2014), 199–209. DOI | RG
  • R Biggs, CC Remsing, Control systems on three-dimensional Lie groups: equivalence and controllability. J. Dyn. Control Syst. 20(3)(2014), 307–339. DOI | RG
  • 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. Link | RG
  • R Biggs, CC Remsing, Cost-extended control systems on Lie groups. Mediterr. J. Math. 11(1)(2014), 193–215. DOI | RG

2013

  • R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, II. Note Mat. 33(2)(2013), 19–31. DOI | RG
  • RM Adams, R Biggs, CC Remsing, Control systems on the orthogonal group SO(4). Commun. Math. 21(2)(2013), 107–128. Link | RG
  • R Biggs, PT Nagy, A classification of sub-Riemannian structures on the Heisenberg groups. Acta Polytech. Hungar. 10(7)(2013), 41–52. DOI | RG
  • R Biggs, CC Remsing, Control affine systems on solvable three-dimensional Lie groups, I. Arch. Math. (Brno) 49(3)(2013), 187–197. DOI | RG
  • 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. DOI | RG
  • 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. DOI | RG
  • RM Adams, R Biggs, CC Remsing, On some quadratic Hamilton-Poisson systems. Appl. Sci. 15(2013), 1–12. Link ​| RG

2012

  • 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. Link | RG
  • RM Adams, R Biggs, CC Remsing, Equivalence of control systems on the Euclidean group SE(2). Control Cybernet. 41(3)(2012), 513–524. Link | RG
  • R Biggs, CC Remsing, A category of control systems. An. St. Univ. Ovidius Constanta 20(1)(2012), 355–368. DOI | RG
  • 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. Link | ​RG

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 | RG
  • R Biggs, CC Remsing, Control systems on three-dimensional Lie groups. Proc. 13th European Control Conference, Strasbourg, France, 2014, 2442–2447. DOI | RG
  • 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 | RG
  • 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 | RG
  • 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 | ​RG
  • 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. RG
  • 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. RG