OpenAI reports a smooth diffeomorphism with simple Lebesgue spectrum
- Mathematics
A C∞ diffeomorphism of the three-torus preserves standard volume and has simple Lebesgue Koopman spectrum on its entire mean-zero L² space.
OpenAI reports a smooth diffeomorphism with simple Lebesgue spectrum
- Mathematics
A C∞ diffeomorphism of the three-torus preserves standard volume and has simple Lebesgue Koopman spectrum on its entire mean-zero L² space.
Curated contributions 1
Understand the problem ↓Understanding the problem
Read the background
A C∞ diffeomorphism of the three-torus preserves standard volume and has simple Lebesgue Koopman spectrum on its entire mean-zero L² space.
Why it matters
If correct, solves the probability-preserving form of Banach’s simple Lebesgue-spectrum problem in smooth dynamics.
What counts as progress
Can a smooth volume-preserving diffeomorphism have simple Lebesgue spectrum on its entire mean-zero space?
Website timeline
Publication dates and editorial changes.
OpenAI reports a smooth diffeomorphism with simple Lebesgue spectrum