Publications

A complete list of our publications and conference proceedings may be found below. In addition, the following papers have been submitted or are in preparation, and may be expected in the near future:

D.I. Barrett, C.E. McLean, C.C. Remsing, Optimal control on the Engel group: extremal controls.
D.I. Barrett, C.E. McLean, C.C. Remsing, Optimal control on the Engel group: extremal trajectories.
D.I. Barrett, C.C. Remsing, On the Schouten and Wagner curvature tensors.
D.I. Barrett, C.C. Remsing, A note on flat nonholonomic Riemannian structures on three-dimensional Lie groups.
D.I. Barrett, C.C. Remsing, Jacobi fields in nonholonomic Riemannian geometry.

Papers

Forthcoming

D.I. Barrett, C.E. McLean, C.C. Remsing, Control systems on the Engel group. To appear in J. Dyn. Control Syst. 25(2019).
D.I. Barrett, C.C. Remsing, On geodesic invariance and curvature in nonholonomic Riemannian geometry. To appear in Publ. Math. Debrecen 94(2019).

2018

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]

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, 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]

2016

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]

2015

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]

2014

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]

2013

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]

2012

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]

2011

C.C. Remsing, Optimal control and integrability on Lie groups. An. Univ. Vest. Timiș. Ser. Mat.-Inform. 49(2)(2011), 101–118. [Link] [RG]

2010

C.C. Remsing, Optimal control and Hamilton–Poisson formalism. Int. J. Pure. Appl. Math. 59(1)(2010), 11–17. [Link] [RG]

Conference Proceedings