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Explore the intricacies of center-unstable foliations and their non-compact leaves in this 35-minute mathematics lecture presented by Jana Rodriguez-Hertz at ICTP Mathematics. Delve into the fundamental properties of these dynamic systems, examining why center-unstable foliations lack compact leaves and the implications of this characteristic. Gain insights into the behavior of these foliations and their significance in the field of dynamical systems and foliation theory.