• Corpus ID: 202719469

Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps

  title={Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps},
  author={Maxwell C. Siegel},
  journal={arXiv: General Mathematics},
  • M. C. Siegel
  • Published 20 September 2019
  • Mathematics
  • arXiv: General Mathematics
It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points of linear operators on spaces of analytic functions. Rather than studying potential fixed points of such operators, we examine their effect on the singularities of functions. To that end, we introduce the notion of a "dreamcatcher", an object which encodes the location and "virtual residue" of the… 
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