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Publication - Dr Thomas Jordan

    Recurrence and transience for suspension flows

    Citation

    Iommi, G, Jordan, TM & Todd, M, 2015, ‘Recurrence and transience for suspension flows’. Israel Journal of Mathematics, vol 209., pp. 547-592

    Abstract

    We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the "renewal flow", which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.

    Full details in the University publications repository