Asymptotic Dynamics and Topology
summary
Conjecture: the topological entropy of a diffeomorphism bounds below the log of the maximal modulus of eigenvalues of its action on homology, so growth on homology predicts dynamical complexity. The talk traces this through the Lefschetz formula and a product-with-circle example that cancels alternating traces, emphasizes the role of homology spectral radius versus alternating sums, cites proven cases for C∞ (Yomdin) and many Axiom A/Morse–Smale examples, and notes the finite regularity (C^r) case remains open.
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