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Watch a 56-minute Aisenstadt Chair lecture series presentation in French and English exploring novel return map approaches for analyzing global dynamics of vibro-impact (VI) pairs. Delve into the study of a ball's movement within a harmonically forced capsule, with applications in VI-based energy harvesting and nonlinear energy transfer. Learn about computationally efficient short-time realizations using "words" that represent key impact sequences and divide state space according to different dynamics. Examine how resulting maps define surfaces that reveal weak and strong attraction to periodic and complex states important for energy output. Discover how reduced piece-wise polynomial approximations create composite maps that capture transients and complement full system bifurcation structure. Understand the framework's application in analyzing stochastically enhanced grazing and bi-stability when noise and attraction scales compete, particularly valuable for cobweb analysis and developing auxiliary maps based on extreme bounds.
