Dynamical systems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-89 Sarnak's Möbius Disjointness Conjecture
- Math-100 Local connectivity of the Mandelbrot set
- Math-101 Density of Hyperbolicity for Rational Maps
- Math-151 Polynomial Bound for Limit Cycles of Planar Polynomial Vector Fields
- Math-176 The Weinstein Conjecture
- Math-188 Furstenberg's x2 x3 conjecture on invariant measures
- Math-216 Morton–Silverman Uniform Boundedness Conjecture
- Math-219 Density of Hyperbolicity for Complex Polynomials
- Math-301 Global Attractor Conjecture for Complex-Balanced Mass-Action Systems
- Math-311 Birkhoff Conjecture (Near-Boundary Continuous Invariant Foliation)
- Math-336 Sinai's Positive Metric Entropy Conjecture for the Chirikov Standard Map
- Math-383 Ivrii conjecture on periodic billiard orbits
- Math-392 Pugh–Shub Stable Ergodicity (C^r Density in Partial Hyperbolicity)
- Math-400 Rokhlin problem on multiple mixing
- Math-424 Lebesgue measure of the boundary of the Mandelbrot set
- Math-449 Shub entropy conjecture
- Math-459 Smooth Realization of Finite-Entropy Ergodic Transformations
- Math-464 Greenfield-Wallach-Katok Conjecture for Cohomology-Free Vector Fields
- Math-466 Pisot Substitution Conjecture
- Math-485 Persistence Conjecture for Weakly Reversible Mass-Action Systems
- Math-488 Zariski Dense Orbit Conjecture
- Math-495 Gottschalk Surjunctivity Problem
- Math-1907 Makienko conjecture
- Math-1908 Completely invariant Fatou components
- Math-1909 Analytic degenerate Herman rings
- Math-1910 Number of degenerate Herman rings
- Math-1934 Generic static-output stabilizability
- Math-1938 Pingree open problems — Hochman problem 2
- Math-1939 Pingree open problems — Boyle problem 1
- Math-1940 Pingree open problems — Boyle problem 2
- Math-1941 Little shift equivalence conjecture
- Math-1942 Classify shifts of finite type
- Math-1943 Factor maps between sofic shifts
- Math-1944 Expansive directions of two-dimensional SFTs
- Math-1945 Commuting expansive automorphisms
- Math-1946 Commuting powers conjecture
- Math-1947 Furstenberg times-p-times-q problem
- Math-1948 Full-support invariant measures
- Math-1949 Invariant measures and subsystems
- Math-1950 Equal-entropy SFT covers
- Math-1951 Equal-entropy subcovers
- Math-1952 Stable cellular-automaton limit sets
- Math-1953 Extension of a block code II
- Math-1954 Embedding one-sided subshifts
- Math-1955 Classify one-sided sofic shifts
- Math-1956 Automorphism groups of full shifts
- Math-1957 Periodic points of cellular automata
- Math-1958 Jointly periodic points in one dimension
- Math-1959 Growth of jointly periodic points I
- Math-1960 Growth of jointly periodic points II