The anti-integrable limit. (English. Russian original) Zbl 1361.37056

Russ. Math. Surv. 70, No. 6, 975-1030 (2015); translation from Usp. Mat. Nauk 70, No. 6, 3-62 (2015).
Summary: The anti-integrable limit is one of the convenient and relatively simple methods for the construction of chaotic hyperbolic invariant sets in Lagrangian, Hamiltonian, and other dynamical systems. This survey discusses the most natural context of the method, namely, discrete Lagrangian systems, and then presents examples and applications.


37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
37B40 Topological entropy
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