... convergence

This upper limit of about 10^-3 varies and depends on the starting value for the iteration, on the "smoothness'' of the stellar input physics, and on the "smoothness'' of the stellar structure. In principle, this is not a limitation of the implicit mass transfer algorithm.

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... converge

This can be proven by using the fact that F is continuous and has only one FP. Thus, $DF(\Delta R) < 0$ for all $\Delta R \in {\rm I\!R}$together with $F(\overline{\Delta R}) = 0$ implies $F \gtrless 0 \Leftrightarrow \Delta R \lessgtr \overline{\Delta R}$so that from (6) the convergence of all solutions to  $\overline{\Delta R}$ can be concluded.

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... field

For details on maps, vector fields an their related nomenclature, the reader is referred to, e.g., Guckenheimer & Holmes (1983).

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... functions

Unimodal functions and their system dynamics are discussed in detail by Collet & Eckmann (1980). For an overview about topological conjugacy and the Feigenbaum scenario see, e.g., Jackson (1989); Thompson & Stewart (1986). For some background about topological conjugacy and topological equivalence of maps, see Wiggins (1990); Arnold (1983). A more in-depth discussion of map (17) can also be found in Büning (2003).

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... parameter

$f_\delta$ is not topologically conjugated to a full family of $\cal S$-unimodal functions. Hence, unlike the logistic map, $f_\delta$ formally does not undergo a complete Feigenbaum scenario.

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... Chaos''

The term "Controlling Chaos'' comes from an article of the same title by Ott et al. (1990) who suggested to control chaotic motion in nonlinear systems by small perturbations. The keyword "Controlling Chaos'' or "Control of Chaos'' later became common in that special field of research. In their introduction to The Control of Chaos: Theory and Applications, Boccaletti et al. (2000) gave a short historical overview of that topic.

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