Supervisor: Dr Ian Morris
Project description:
In the 1970s and 1980s the emerging discipline of chaos theory was substantially boosted by the importation of variational methods originating in statistical physics in the form of the thermodynamic formalism of Ruelle, Bowen and Sinai. In the following decades these techniques have seen powerful applications across a broad swath of mathematics including conformal fractal geometry, hyperbolic geometry, group theory and combinatorics as well as the study of dynamical systems and mathematical physics. This project aims to extend these methods to the study of measures which maximise Lyapunov exponents of linear cocycles in place of the Birkhoff average which is maximised in the classical theory, permitting applications to control theory, non-conformal fractal geometry and the theory of random matrix products.
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