This proposal requests funding for US-based participants to attend the conference "Global Dynamics Beyond Uniform Hyperbolicity" which will be held at the Banach Center in Bedlewo, Poland May 27- June 7, 2013. This conference is sixth in a series of international conferences held since 2001, two of which were held in the US and funded primarily by the NSF. The conference will focus on the global qualitative study (topological and ergodic) of differentiable dynamical systems, especially diffeomorphisms and vector fields, that are not uniformly hyperbolic. Among the main topics to be covered are: -Beyond Hyperbolicity: Partial hyperbolicity, Nonuniform hyperbolicity, Singular hyperbolicity, Lyapunov exponents, Dimension, Statistical properties. -Global and Semilocal Properties: The C1-topology, Bifurcations. -Other Topics: Interval Dynamics, Foliations.
This study of smooth dynamical systems has its origins in early efforts to establish the stability of the solar system. Early pioneers such as Henri Poincare and George Birkhoff discovered mechnanisms for stability and instability, thus initiating the study of hyperbolic dynamical systems. Around the same time, the geometer Eberhard Hopf used hyperbolic methods to study the long-term behavior of geodesics (straight lines) in negatively curved spaces (such as those modelled on Minkowski space). A century later, the study of hyperbolic dynamical systems has blossomed into a mature field, one of the cornerstones of dynamics. This conference, one in a series held every few years, brings together a truly international group of experts, representing 5 continents, to explore the latest developments beyond hyperbolicity. Exposure to this cutting edge work through these workshops has spurred research advances in a previous generation of US graduate students, many of whom will speak at this workshop. Previous incarnations of this workshop have also led to international collaborative teams, and we anticipate future benefits of a similar nature.
which was held at the Banach Center in Bedlewo, Poland May 27- June 7, 2013. This conference was the sixth in a series of international conferences held since 2001, two of which were held in the US and funded primarily by the NSF. The conference was focused on so-called nonlinear problems in smooth dynamics, whose appications are tied to understanding concrete problems in planetary motion, mixing in inhomogeneous media, and deep mathematical problems in related areas such as geometry and number theory. The workshop combined carefully chosen plenary lectures, aimed at the general audience, with specialized afternoon sessions. The broader impacts of these activities are tied to the interdisciplinary nature of the participant base, the large numbers of junior researchers who attended, and the synergy generated by interactions between these groups. The funds were used to pay the travel and local expenses for the following US-based participants: Brown, Aaron Chaika, Jon Climenhaga, Vaughn Erchenko, Elena Fisher, Todd Gekhtman, Ilya Gerber, Marlies Gogolev, Andrey Hasselblatt, Boris Hurder, Steve Katok, Anatole (Minicourse Lecturer) Katok, Svetlana Ledrappier, Francois Newhouse, Sheldon Nicol, Matthew Parwani, Kamlesh Pesin, Yakov Pugh, Charles Torok, Andrew Varao José Régis Vishnepolsky, Rachel Visscher, Dan Wang, Zhiren Xia, Jeff Xue, Jinxin Zhang, Hong Kun Five of these participants are female, and the majority do not have individual research grants. Many of these participants spoke at the conference, including the young researcher Jinxin Xue, who announced his recent solution with Dmitry Dolgopyat of the existence of non-collision singularities in the three body problem, a case of the celibrated Painleve conjecture. The conference was judged to be a complete success and a fllow-conference is planned for 2015 in Chile.