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Some open problems in dynamical systems. (English) Zbl 0910.58036

The author gives a list of open problems in dynamical systems, divided into 7 parts:
1. Siegel singular disks,
2. Invariant tori,
3. Questions of measure preserving diffeomorphisms on 2-manifolds,
4. Entropy and exponents,
5. Existence of periodic orbits,
6. Instabilities of the Hamiltonian flow on \(T^*T^n\), \(n \geq 3\), and the problem of topological stability,
7. The oldest open problem in dynamical systems (the problems here are connected with n-body problems and bounded orbits).

MSC:

58-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis
37A99 Ergodic theory
37C10 Dynamics induced by flows and semiflows
70F10 \(n\)-body problems
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