This study investigates the behavior of a damped, inelastic, sinusoidally forced impact oscillator which has its barrier placed such that the oscillator always vibrates under compression about its subharmonic resonant frequencies. The Poincaré sections at near subharmonic resonance conditions exhibit finger-shaped chaotic attractors, similar to the strange attractor mapping of Hénon and the ones found by Holmes in his study of chaotic resonances of a buckled beam. The number of such fingers are observed to increase as the barrier distance from the equilibrium is decreased. These chaotic states are interspersed with regimes of periodic behavior, with the periodicity being in accordance with well defined period adding laws. This study also focuses on the ordered behavior of the one-impact period-[Formula: see text] orbits around the higher subharmonics of the oscillator.

中文翻译：

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预应力、谐波激励、振动冲击振荡器在次谐波谐振处的分岔

本研究调查了阻尼、非弹性、正弦强制冲击振荡器的行为，该振荡器的屏障放置使得振荡器始终在其次谐波谐振频率的压缩下振动。近次谐波共振条件下的庞加莱截面呈现出手指状的混沌吸引子，类似于 Hénon 的奇怪吸引子映射以及 Holmes 在他研究弯曲梁的混沌谐振时发现的那些。观察到这种手指的数量随着与平衡的势垒距离的减小而增加。这些混沌状态散布着周期性行为的机制，周期性符合明确定义的周期添加定律。本研究还关注单次冲击时期的有序行为——[公式：