  This paper helps to clarify the status of cylindrical contact homology, a
conjectured contact invariant introduced by Eliashberg, Givental, and Hofer in
2000. We explain how heuristic arguments fail to yield a well-defined
homological invariant in the presence of multiply covered curves. We then
introduce a large subclass of dynamically convex contact forms in dimension 3,
termed dynamically separated, and demonstrate automatic transversality holds,
therby allowing us to define the desired chain complex. The Reeb orbits of
dynamically separated contact forms satisfy a uniform growth condition on their
Conley-Zehnder index under iteration, typically up to large action; see
Definition 1.15 These contact forms arise naturally as perturbations of
Morse-Bott contact forms such as those associated to $S^1$-bundles. In
subsequent work, we give a direct proof of invariance for this subclass and,
when further proportionality holds between the index and action, powerful
geometric computations in a wide variety of examples.
