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A computer-assisted approach to small-divisors problems arising in Hamiltonian mechanics. (English) Zbl 0820.70004
Computer aided proofs in analysis, Proc. IMA Participating Inst. Conf., Cincinnati/OH (USA), IMA Vol. Math. Appl. 28, 43-51 (1991).
[For the entire collection see Zbl 0741.00031.]
We discuss, with special emphasis on the role of computers, some new results in title problem. In particular, we show that, although mechanical computations allow to establish rigorous results, there are intrinsic difficulties in proving computer-assisted theorems whose proofs are based on algorithms involving a lot of divisions by small quantities.

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70H99 Hamiltonian and Lagrangian mechanics
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems