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Daofei Zhang

About me

My name is Daofei Zhang (张道飞), and I am a third-year PhD student of Prof. Mark PollicottLink opens in a new window. I am interested in decay of correlations for skew products of hyperbolic flows.

Previously, I am a graduate student of Prof. Dawei YangLink opens in a new window in Suzhou University, and my research topic is singular hyperbolic flows and their volume properties.

Contact

Email: Daofei dot Zhang at warwick dot ac dot uk

A brief description of my research project

Many years ago, Bowen, Ruelle and Sinai, etc., established a theory of hyperbolic dynamical systems. Hyperbolic systems have many interesting properties, one of which is the rate of mixing (also known as the decay of correlation). For continuous-time hyperbolic systems (i.e. hyperbolic flows), unlike discrete-time hyperbolic systems (i.e. hyperbolic diffeomorphisms) are automatically exponentially mixing with respect to equilibrium states, estimating their rate of mixing is more difficult. In this direction, Dolgopyat has made outstanding contributions. Beyond uniform hyperbolicity, skew products of hyperbolic systems have attracted much attention because they provide one of the simplest examples of weakly hyperbolic systems. For skew products of hyperbolic diffeomorphisms, the rate of mixing was studied by Dolgopyat. For skew products of hyperbolic flows, the research of the rate of mixing will become more complicated, and my research project is trying to make some contributions in this direction.

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