Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
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We study the rectilinear motion of a mass point with impacts against a stopper. The motion between the impacts is described by a second-order ordinary differential equation with a parameter. The impact recovery coefficient also depends on the parameter of the vibroimpact system. We describe a bifurcation that leads to the generation of a Smale horseshoe in a parametric neighborhood of the chatter phenomenon. We prove the existence of an invariant set described by symbolic dynamics.
KeywordsInitial Data Unstable Manifold Stable Manifold Symbolic Dynamic Impact Time
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- 1.Kryzhevich, S.G., Chaos in Vibroimpact Systems with One Degree of Freedom in a Neighborhood of Chatter Generation. I, Differ. Uravn., 2010, vol. 46, no. 10, pp. 1403–1408.Google Scholar
- 4.Smale, S., Diffeomorphisms with Many Periodic Points, in Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton: Princeton Univ., 1965, pp. 63–80.Google Scholar
- 5.Palis, J. and de Melo, W., Geometric Properties of Dynamical Systems. An Introduction, New York: Springer, 1982. Translated under the title Geometricheskaya teoriya dinamicheskikh sistem. Vvedenie, Moscow: Mir, 1986.Google Scholar