Basic facts and naive questions (Q6601736)

The author reflects on his continuing desire to identify geometric reasons underlying the KAM theorem, and other results relating to Arnold's many conjectures. He refers to the papers of Claude Viterbo, to whom his paper is dedicated. These are [\textit{C. Viterbo}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4, 337--356 (1987; Zbl 0631.58013); Math. Ann. 292, No. 4, 685--710 (1992; Zbl 0735.58019)]. More broadly, the author is following up on several of the Arnold conjectures especially those related to Poincaré's ``last geometric theorem''.\N\NHe indicates his discomfort with the abstraction associated with results based on Floer theory and his desire to find more ``down-to-earth'' approaches closer to the underlying geometry.\N\NThe questions addressed include subharmonic bifurcations -- in real or complex dimension one, in the holomorphic case, with Arnold tongues and KAM circles, and finally in higher dimensions.\N\NFor the entire collection see [Zbl 1515.53004].