Dynamics Seminar: Fall 2006

The Dynamics seminar will meet on Friday afternoons at 2:30 in Clearihue A204. All are welcome. The list of seminars is as follows. For further information, please contact me at  

Date Speaker Title:
22/9 Arek Goetz (San Francisco State University) The microscopic and macroscopic world of piecewise isometric dynamical systems
29/9 Anthony Quas (UVic) Joinings and d-bar distance in Ergodic Theory
6/10 Anthony Quas(UVic) Joinings and d-bar distance in Ergodic Theory II
13/10 Michael Baake (Bielefeld) Snapshots from diffraction theory
20/10 Nicolae Strungaru (UVic) From point sets to Dynamical Systems 
27/10 Nicolae Strungaru (UVic) From point sets to Dynamical Systems II 
3/11 Chris Bose (UVic) Young Towers, Intermittency and the Generalized Baker's Transformation
10/11 Chris Bose (UVic) Young Towers, Intermittency and the Generalized Baker's Transformation II
17/11 No seminar
24/11
1/12

Date: 22/9
Speaker: Arek Goetz (San Francisco State University)
Title: The microscopic and macroscopic world of piecewise isometric dynamical systems
Abstract: In this talk we illustrate the complexity of two dimensional generalizations of interval exchange transformations by surveying examples in the literature as well as by simulating on the computer Poincare Recurrence Maps.
Date: 29/9 and 6/10
Speaker: Anthony Quas (UVic)
Title: Joinings and d-bar distance in Ergodic Theory
Abstract: Joinings may be seen as a generalization of measure-theoretic isomorphisms between two dynamical systems. They also provide a convenient way of defining the important d-bar distance between two dynamical systems. We consider this in the classical context of g-measures.
Date: 13/10
Speaker: Michael Baake (Bielefeld)
Title: Snapshots from diffraction theory
Abstract: I plan to (very informally) summarize some recent developments in this area, with examples both from perfect and random order. Time permitting, I might say a few words on pinwheel diffraction.
Date:20/10 and 27/10
Speaker:Nicolae Strungaru (UVic)
Title:From point sets to Dynamical Systems
Abstract: Starting with a point set (which represents the idealization of the positions set of atoms in a real solid), one can take the closure of its translates in a suitable topology and create a Dynamical system. In this talk we will introduce two different topologies, one based on local pattern and the other based by statistical coincidence and see how one can get information about the point set by studying the corresponding Dynamical system. We finish by showing the differences between the two topologies, and explaining in which cases they are similar.
Date:
Speaker:Chris Bose (UVic)
Title:Young Towers, Intermittency and the Generalized Baker's Transformation
Abstract:Birkhoff's theorm states that (almost every) orbit of a dynamical system will display time averages consistent with a given (ergodic) invariant measure for the system. However, there are a number of ways in which this could happen. One of the more curious is through something termed intermittency: from time to time orbits get trapped in an unreasonably small part phase space for an unreasonably long time, then suddenly (randomly?) escape and return to more uniform behaviour. These 'intermittent' bouts of inconsistent behavior necessarily occur on widely separated parts of the orbit in order to maintain good average statistics. A quick search by Google shows that such behavior is of great interest in both theoretical and applied dynamics. In the first talk I will show a very easy way to build intermittent maps in both the invertible (non-uniformly hyperbolic) and non-invertible (non-uniformly expanding) setting using the generalized baker's transformation. A key question for these maps in both the specific and general setting is the rate of correlation decay. A self-contained construction can tease this out for the GBT maps. In the second part I will describe a powerful, general construction due to L.S. Young (1998) which has proved to be THE correct way to approach these delicate calculations on non-uniformly hyperbolic systems. The GBT maps from the first part will provide convenient examples to illustrate and check the computations performed by the general machinery. This is joint work with Rua Murray. Rua has recently produced a set of movies(!) to illustrate some of this, and which I hope to get running in time for the talks.
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For previous semesters, see
Spring 2006