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Appendix A Notation

Symbol Description Location
\(G\) Lie group Definition 2.1
\(\mathfrak{g}\) Lie algebra of a Lie group Definition 2.1
\(V_1\oplus\dots\oplus V_s\) stratification of a Lie algebra Definition 2.1
\(\delta_{\dilationfactor}\) dilation by a factor \(\dilationfactor\in\RR\) Definition 2.2
\(\norm{\cdot}_d\) projection norm associated with a homogeneous distance Definition 2.4
\(L_g\) left-translation by a group element \(g\in G\) Definition 2.9
\(u\) control of a horizontal curve Definition 2.9
\(\gamma_\dilationfactor\) a curve dilated and reparametrized by a factor \(\dilationfactor>0\) Lemma 2.12
\(\partial E(Y)\) family of subdifferentials of a function \(E\) at a point \(Y\) Definition 2.17