Speaker: Dr. Masazumi Honda, University of Cambridge

ORC would like to encourage you to attend the seminar by Dr Sai, National Institutes of Radiological Sciences (Chiba, Japan). At the end of his talk, he will present some opportunities for using NIRS infrastructure in physics and biology research.

A blender is an intricate geometric structure of a three- or higher-dimensional diffeomorphism. Its characterising feature is that its invariant manifolds behave as geometric objects of a dimension that is larger than expected from the dimensions of the manifolds themselves. We introduce a family of three-dimensional Hénon-like maps and study how it gives rise to an explicit example of a blender. The map has two saddle fixed points. Their associated stable and unstable manifolds consist of points for which the sequence of images or pre-images converges to one of the saddle points; such points lie on curves or surfaces, depending on the number of stable eigenvalues of the Jacobian at the saddle points. We employ advanced numerical techniques to compute one-dimensional stable and unstable manifolds to very considerable arclengths. In this way, we not only present the first images of an actual blender but also obtain a convincing numerical test for the blender property. This allows us to present strong numerical evidence for the existence of the blender over a larger parameter range, as well as its disappearance and geometric properties beyond this range. We will also discuss the relevance of the blender property for chaotic attractors; joint work with Stephanie Hittmeyer and Bernd Krauskopf (University of Auckland) and Katsutoshi Shinohara (Hitotsubashi University).

The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This talk addresses the role of the stable and unstable manifolds in organising the dynamics more globally. A main object of interest is the stable manifold of the origin of the Lorenz system, also known as the Lorenz manifold. This two-dimensional manifold and associated manifolds of saddle periodic orbits can be computed accurately with numerical methods based on the continuation of orbit segments, defined as solutions of suitable two-point boundary value problems. We use these techniques to give a precise geometrical and topological characterisation of global manifolds during the transition from simple dynamics, via preturbulence to chaotic dynamics, as the Rayleigh parameter of the Lorenz system is increased; joint work with Hinke Osinga (University of Auckland) and Eusebius Doedel (Concordia University, Montreal). 

Dr. Aleksandra Budra, Assistant Professor, Erasmus University Medical Center Rotterdam. Language: English

Professor Sergiusz Jóźwiak, Warsaw Medical University, and The Children’s Memorial Health Institute, Warsaw, Poland. Language: English

Dr. Marc Bescond, LIMMS CNRS-IIS The University of Tokyo

Dr. Atsushi Takahara, Professor at Kyushu University

¹JST ERATO Takahara Soft Interfaces Project
²International Institute for Carbon-Neutral Energy Research (I²CNER), Kyushu University
³Institute for Materials Chemistry and Enginering, Kyushu Universtity

Speaker:
By Dr Joshua Goldberg, Department of medical Neurobiology, The Hebrew University of Jerusalem     http://joshgoldberg.ekmd.huji.ac.il

Prof. Ada Yonath, Nobel Laureate in chemistry 2009, Weizmann Institute of Science

Language: English