Notes on the notation

Welcome to The Machine!
Pink Floyd, LP ``Wish You Were Here'' (1975)

scalar numbers -

italic letters, e.g., n (dimension of phase space), m (dimension of parameter space), indices i and j, time t, period T, radius R.

vector data -

bold letters, sometimes indexed, e.g., x (current state of the dynamical system), v (some velocity vector), normal  n, initial condition  s, critical points  c_i.

vector components -

vector (bold letter) indexed by the use of squared brackets, e.g., v[1], n[i].

sets, spaces, manifolds -

standard labels for predefined sets, e.g., R (real numbers) and C (complex numbers); capital Greek letters for special subsets, etc., e.g., phase space  $\Omega\subseteq\mathbf{R}^3$ or parameter space  $\Pi\subseteq\mathbf{R}^m$; calligraphic letters for curves, surfaces, manifolds, e.g., trajectory  $\mathcal{T}_\mathbf{s}$, cycles  $\mathcal{C}_i$.

functions, mappings, parameterizations -

embraced functional arguments, e.g., trajectory  $\mathcal{T}_\mathbf{s}(t)$, dynamical system specification  f_p(x,t), Poincaré map  p(x).

dependence on parameters -

parameter(s) as indices, for instance, f_p.

matrices -

bold upper case letters, e.g., Jacobian $\bf {}J$, $\bf {}A$.

mailto:helwig@cg.tuwien.ac.at.