This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016.

Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo's co-authors and former doctoral students.

Sadly, 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 an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field.

Inhalt
J. Palis and F. Lenarduzzi, Welington de Melo and Jacob Palis: their first meeting, some of their work on structural stability and a lifetime of friendship.- E. de Faria and S. van Strien, Welington de Melo (1946-2016).- A. Avila and V. Delecroix, Some monoids of Pisot matrices.- P. Brandao, J. Palis, V. Pinheiro, On the statistical attractors and attracting Cantor sets for piecewise smooth maps.- S. Bullett, L. Lomonaco and C. Siqueira, Correspondences in complex dynamics.- A. de Carvalho and T. Hall and P. Hazard, Braid quivalence in the Henon Family I.- E. Catsigeras, Empiric stochastic stability of physical and pseudophysical measures.- L. J. Diaz and S. A. Perez, Blender-horseshoes in center-unstable Henon-like families.- E. de Faria, P. Hazard and C. Tresser; Growth, topological entropy, slow entropy, equicontinuity, topological complexity.- J. Epperlein, D. Kwietniak, P. Oprocha, Mixing properties in coded systems.- G. Levin, W. Shen and S. van Strien, Transversality forcritical relations of families of rational maps: an elementary proof.- J. Rodriguez Hertz, R. Ures, On the three-legged accessibility property.- L. Salgado, V. Coelho, Adapted metrics for codimension one singular hyperbolic flows.- M. Stadlbauer, On conformal measures and harmonic functions for group extensions.- M. Yampolsky and J. Yang, The boundaries of golden-mean Siegel disks in the complex quadratic Henon family are not smooth.- Wellington's photos from childhood to academic life.