报告题目: |
Parametrization of the Ergodic Partition Using Time-Averages of Observables |
报告人: |
Marko Budisic |
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报告时间: |
2009-12-21 14:30 |
报告地点: |
物理系三楼报告厅 |
主办单位: |
物理系 |
简介: |
内容提要：
Ergodic partition of a measure-preserving dynamical system is the
finest partition of the state space into invariant sets. Dynamics
inside each element of the ergodic partition is ergodic, i.e., two
trajectories within the ergodic set have the same statistical
behavior. To compute the ergodic partition, we use functions
constructed as time-averages of observables along trajectories. Such
functions are invariants of motion, and, therefore, their level sets
form invariant partitions. Starting from a function basis as the set
of observables, we form their time-averages, and then apply a machine
learning technique, the Diffusion Maps algorithm, to extract
parametrization of the ergodic partition by aggregating trajectories
into ergodic sets. The resulting parametrization could have a range of
potential applications: from exploratory analysis of an unknown
system, in terms of visualization and behavior identification, to more
rigorous applications, such as design of controls and
control-theoretic analysis of systems.
报告人简介：
Marko Budisic graduated in 2006 with a diploma in Electrical
Engineering with emphasis on Automatic Control from University of
Zagreb, Croatia. In Fall 2006, he joined the PhD program in Mechanical
Engineering at University of California, Santa Barbara. Currently, he
is a PhD Candidate working with Dr. Igor Mezic, at UC Santa Barbara.
Marko's research interests lie in the theory of dynamical systems,
with focus on using ergodic theory and operator theory to address
issues that are difficult to resolve using geometric methods.
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