Work in progress
- D.I. Barrett, C.C. Remsing, On a family of homogeneous spaces.
- C.C. Remsing, Invariant foliations on homogeneous spaces.
- C.C. Remsing, One-dimensional foliations on compact homogeneous spaces.
- C.C. Remsing, Some remarks on Lorentzian flows on homogeneous spaces.
Papers
2023
- D.I. Barrett, C.C. Remsing, On the Schouten and Wagner curvature tensors. Rend. Circ. Mat. Palermo 72(2)(2023), 565--590. [DOI] [RG]
- D.I. Barrett, C.C. Remsing, Restricted Jacobi fields. Internat. Electr. J. Geom. 14(2)(2021), 247--265. [DOI] [RG]
- D.I. Barrett, C.C. Remsing, A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups. Beitr. Algebra Geom. 60(2019), 419--436. [DOI] [RG]
- D.I. Barrett, C.E. McLean, C.C. Remsing, Control systems on the Engel group. J. Dyn. Control Syst. 25(3)(2019), 377--402. [DOI] [RG]
- D.I. Barrett, C.C. Remsing, On geodesic invariance and curvature in nonholonomic Riemannian geometry. Publ. Math. Debrecen 94(1-2)(2019), 197--213. [DOI] [RG]
- D.I. Barrett, R. Biggs, C.C. Remsing, Quadratic Hamilton–Poisson systems on \(\mathfrak{se}\mathsf{(1,1)}^*_-\): The inhomogeneous case. Acta Appl. Math. 154(2018), 189–230. [DOI] [Online PDF] [RG]
- R. Biggs, Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups. Commun. Math. 25(2017), 99–135. [DOI] [RG]
- R. Biggs, C.C. Remsing, Invariant control systems on Lie groups: a short survey. Extracta Math. 32(2017), 213–238. [Online PDF] [RG]
- R. Biggs, C.C. Remsing, Invariant control systems on Lie groups. In: G. Falcone (ed.), Lie Groups, Differential Equations, and Geometry: Advances and Surveys, Springer, pp. 127–181. [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]
- C.E. Bartlett, R. Biggs, C.C. Remsing, Control systems on nilpotent Lie groups of dimension ≤ 4: equivalence and classification. Differential Geom. Appl. 54(2017), 282–297. [DOI] [RG]
- R. Biggs, C.C. Remsing, Quadratic Hamilton–Poisson systems in three dimensions: equivalence, stability, and integration. Acta Appl. Math. 148(2017), 1–59. [DOI] [Online PDF] [RG]
- C.E. Bartlett, R. Biggs, C.C. 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.M. Adams, R. Biggs, W. Holderbaum, C.C. Remsing, Stability and integration of Hamilton–Poisson systems on \(\mathfrak{so} \mathsf{(3)}^*_-\). Rend. Mat. Appl. 37(2016), 1–42. [Link] [RG]
- R. Biggs, C.C. Remsing, Equivalence of control systems on the pseudo-orthogonal group \(\mathsf{SO(2,1)}\). An. Ştiint. Univ. Ovidius Constanta. 24(2)(2016), 45–65. [DOI] [RG]
- D.I. Barrett, R. Biggs, C.C. Remsing, O. Rossi, Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. J. Geom. Mech. 8(2)(2016), 139–167. [DOI] [RG]
- R. Biggs, P.T. Nagy, On sub-Riemannian and Riemannian structures on the Heisenberg groups. J. Dyn. Control Syst. 22(2016), 563–594. [DOI] [RG]
- R. Biggs, C.C. Remsing, On the classification of real four-dimensional Lie groups. J. Lie Theory. 26(2016), 1001–1035. [Link] [RG]
- R. Biggs, P.T. Nagy, On extensions of sub-Riemannian structures on Lie groups. Differential Geom. Appl. 46(2016), 25–38. [DOI] [RG]
- M.A. Henning, V. Naicker, Bounds on the disjunctive total domination number of a tree. Discuss. Math. Graph Theory 36(2016), 153–171. [DOI]
- M.A. Henning, V. Naicker, Disjunctive total domination in graphs. J. Comb. Optim. 31(3)(2016), 1090–1110. [DOI] [arXiv]
- C.E. Bartlett, R. Biggs, C.C. Remsing, Control systems on the Heisenberg group: equivalence and classification. Publ. Math. Debrecen 88(1-2)(2016), 217–234. [Link] [RG]
- D.I. Barrett, R. Biggs, C.C. Remsing, Affine distributions on a four-dimensional extension of the semi-Euclidean group. Note Mat. 35(2)(2015), 81–97. [DOI] [RG]
- R. Biggs, C.C. Remsing, On the equivalence of control systems on Lie groups. Commun. Math. 23(2)(2015), 119–129. [Link] [RG]
- M.A. Henning, V. Naicker, Graphs with large disjunctive total domination. DMTCS 17(1)(2015), 255–282. [Link] [arXiv]
- R. Biggs, C.C. 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]
- D.I. Barrett, R. Biggs, C.C. Remsing, Quadratic Hamilton–Poisson systems on \(\mathfrak{se}\mathsf{(1,1)^*_-}\): the homogeneous case. Int. J. Geom. Methods Mod. Phys. 12(2015), 1550011 (17 pages). [DOI] [RG]
- R. Biggs, C.C. Remsing, Some remarks on the oscillator group. Differential Geom. Appl. 35(2014), 199–209. [DOI] [RG]
- R. Biggs, C.C. Remsing, Control systems on three-dimensional Lie groups: equivalence and controllability. J. Dyn. Control Syst. 20(3)(2014), 307–339. [DOI] [RG]
- D.I. Barrett, R. Biggs, C.C. Remsing, Affine subspaces of the Lie algebra \(\mathfrak{se}\mathsf{(1,1)}\). Eur. J. Pure Appl. Math. 7(2)(2014), 140–155. [Link] [RG]
- R. Biggs, C.C. Remsing, Cost-extended control systems on Lie groups. Mediterr. J. Math. 11(1)(2014), 193–215. [DOI] [RG]
- R. Biggs, C.C. Remsing, Control affine systems on solvable three-dimensional Lie groups, II. Note Mat. 33(2)(2013), 19–31. [DOI] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, Control systems on the orthogonal group \(\mathsf{SO(4)}\). Commun. Math. 21(2)(2013), 107–128. [Link] [RG]
- R. Biggs, P.T. Nagy, A classification of sub-Riemannian structures on the Heisenberg groups. Acta Polytech. Hungar. 10(7)(2013), 41–52. [DOI] [RG]
- R. Biggs, C.C. Remsing, Control affine systems on solvable three-dimensional Lie groups, I. Arch. Math. (Brno) 49(3)(2013), 187–197. [DOI] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, Two-input control systems on the Euclidean group \(\mathsf{SE(2)}\). ESAIM: Control Optim. Calc. Var. 19(4)(2013), 947–975. [DOI] [RG]
- R. Biggs, C.C. Remsing, Control affine systems on semisimple three-dimensional Lie groups. An. Ştiint. Univ. “A.I. Cuza” Iași Mat. 59(2)(2013), 399–414. [DOI] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, On some quadratic Hamilton–Poisson systems. Appl. Sci. 15(2013), 1–12. [Link] [RG]
- R. Biggs, C.C. Remsing, A note on the affine subspaces of three-dimensional Lie algebras. Bul. Acad. Ştiinte Repub. Mold. Mat. 2012, no. 3, 45–52. [Link] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, Equivalence of control systems on the Euclidean group \( \mathsf{SE(2)}\). Control Cybernet. 41(3)(2012), 513–524. [Link] [RG]
- C.C. Remsing, Optimal control on the rotation group \(\mathsf{SO(3)}\). Carpathian J. Math. 28(2)(2012), 305–312. [PDF] [RG]
- R. Biggs, C.C. Remsing, A category of control systems. An. St. Univ. Ovidius Constanta 20(1)(2012), 355–368. [DOI] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, Single-input control systems on the Euclidean group \(\mathsf{SE(2)}\). Eur. J. Pure Appl. Math. 5(1)(2012), 1–15. [Link] [RG]
Conference Proceedings
2014
- D.I. Barrett, R. Biggs, C.C. 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, 2466–2471. [DOI] [RG]
- R. Biggs, C.C. Remsing, Control systems on three-dimensional Lie groups. Proc. 13th European Control Conference, Strasbourg, France, 2442–2447. [DOI] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, Quadratic Hamilton–Poisson systems on \(\mathfrak{so}\mathsf{(3)^*_-}\): classification and integration. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 55–66. [RG]
- R. Biggs, C.C. Remsing, A classification of quadratic Hamilton–Poisson systems in three dimensions. Proc. 15th International Conference on Geometry, Integrability and Quantization, Varna, Bulgaria, 67–78. [RG]
- R. Biggs, C.C. Remsing, Feedback classification of invariant control systems on three-dimensional Lie groups. Proc. 9th IFAC Symp. Nonlinear Control Syst., Toulouse, France, 506–511. [PDF] [RG]
- R. Biggs, C.C. Remsing, On the equivalence of cost-extended control systems on Lie groups. Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal, 60-65. [PDF] [RG]
- R.M. Adams, R. Biggs, C.C. Remsing, On the equivalence of control systems on the orthogonal group \( \mathsf{SO(4)} \). Proc. 8th WSEAS Internat. Conf. Dyn. Syst. Control, Porto, Portugal, 54–59. [PDF] [RG]
