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.
Table of Contents
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 for critical 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.