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This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, celebrating the 70th anniversary of Welington de Melo, which was held at IMPA, Rio de Janeiro, in November 2016, and highlights the most recent results in one-dimensional dynamics and its applications.
The volume was intended to be a collection of contributions celebrating the highly successful meeting, which brought together experts in this field, many of Welington de Melo's co-authors and all his former doctoral students.
Unfortunately Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly important, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are mandatory references for beginners in this area.