Classical Mathematical Physics: Dynamical Systems and Field Theories
by Walter Thirring [son of Hans Thirring, who was the co-discoverer of the Lense-Thirring frame effect in general relativity]
(Preface to the second edition).
Since the first edition already contained plenty of material for a one-semester course, new material was added only when some of the original could be dropped or simplified. (…) This involved not only the use of more refined mathematical tools, but also a reevaluation of the word fundamental. What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler’s laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order. These irrational numbers are precisely the ones that are the least well approximated by rationals, and orbits with radii having these ratios are the most robust against each other’s perturbations, since they are the least affected by resonance effects.