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Chaotic dynamics in a simple class of Hamiltonian systems with applications to a pendulum with variable length. (English) Zbl 1240.37039
Chaotic dynamics are proved for the Poincaré map along the trajectories of the system equivalent to the equation $$x''+cx'+q(t)f(x)=0$$, where $$q$$ is a periodic function of constant sign. One theorem concerns the frictionless case, where $$c=0$$, at the second one the friction is present ($$c\neq 0$$).

##### MSC:
 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
##### Keywords:
chaotic dynamics; pendulum; Poincaré map