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Dynamics & Analysis · 5 problems

Open problems in Dynamics & Analysis

Every Dynamics & Analysis problem in the Math Lab index — 5 in all. Each carries a precise statement, an honest status (open means open), and a concrete plan for throwing compute or tokens at it.

Berry–Tabor conjectureDynamics & Analysisuntouched

The energy-level spacings of a generic quantized integrable system follow Poisson statistics — in contrast to random-matrix statistics for chaotic systems.

Birkhoff conjecture on integrable billiardsDynamics & Analysisuntouched

If the billiard dynamics inside a smooth convex curve is integrable (foliated by caustics), the curve must be an ellipse.

Outer billiards unboundednessDynamics & Analysisuntouched

For which convex shapes does the outer (dual) billiard map admit unbounded orbits? Moser asked whether orbits can escape to infinity at all.

Regularity & blow-up in model fluid equationsDynamics & Analysisuntouched

Do smooth solutions of simplified fluid models (1D model equations, axisymmetric Euler scenarios, generalized SQG) blow up in finite time — and what does the blow-up profile look like?

Sendov's conjectureDynamics & Analysisuntouched

If all roots of a polynomial lie in the closed unit disk, then within distance 1 of each root lies a critical point (root of the derivative).

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