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Titlebook: Nonlinear Science and Complexity; J.A. Tenreiro Machado,Albert C.J. Luo,Lino B. Figu Book 2011 Springer Science+Business Media B.V. 2011 N

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Periodic and Chaotic Motions in a Gear-pair Transmission System with Impactsl with possible stick between the two gears. Based on the mapping structures, periodic motions of such a system are predicted analytically. To understand the global dynamical behaviors of the gear transmission system, system parameter maps are developed. Numerical simulations for periodic and chaotic motions are performed from the parameter maps.
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Group-Invariant Solutions of Fractional Differential EquationsIn this paper, the results of symmetry analysis for some nonlinear fractional differential equations are presented. Applications of the symmetries for constructing exact solutions are illustrated.
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Conserved Forms of Second Order-Ordinary Differential EquationsIn this paper we prove that .-symmetries of any second-order ordinary differential equation can be used to construct an integrating factor of the equation, and that the associated conserved form can be derived from the algorithm of reduction associated to the .-symmetry.
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