OpenAI reports a C¹ counterexample to Shub’s entropy conjecture
- Mathematics
A noninvertible C¹ self-map of a compact smooth manifold without boundary has zero topological entropy while its induced action on second real homology has eigenvalue 2.
OpenAI reports a C¹ counterexample to Shub’s entropy conjecture
- Mathematics
A noninvertible C¹ self-map of a compact smooth manifold without boundary has zero topological entropy while its induced action on second real homology has eigenvalue 2.
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Read the background
A noninvertible C¹ self-map of a compact smooth manifold without boundary has zero topological entropy while its induced action on second real homology has eigenvalue 2.
Why it matters
If correct, disproves the general C¹ self-map formulation of Shub’s entropy conjecture.
What counts as progress
Must a C¹ self-map’s entropy exceed the logarithm of its homological spectral radius?
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OpenAI reports a C¹ counterexample to Shub’s entropy conjecture