Free energy and equilibrium states for families of interval maps / Neil Dobbs, Mike Todd.
| Author/creator | Dobbs, Neil |
| Other author | Todd, Mike (Professor of mathematics) |
| Format | Electronic |
| Publication Info | Providence : American Mathematical Society, [2023] |
| Description | v, 103 pages : illustrations ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; Volume 286, Number 1417 (first of 6 numbers) |
| Abstract | "We study continuity, and lack thereof, of thermodynamical properties for onedimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit measure will have free energy at least that of the limit of the free energies. From this, we deduce results concerning existence and continuity of equilibrium states (including statistical stability). Metric entropy, not semicontinuous as a general multimodal map varies, is shown to be upper semicontinuous under an appropriate hypothesis on critical orbits. Equilibrium states vary continuously, under mild hypotheses, as one varies the parameter and the map. We give a general method for constructing induced maps which automatically give strong exponential tail estimates. This also allows us to recover, and further generalise, recent results concerning statistical properties (decay of correlations, etc.). Counterexamples to statistical stability are given which also show sharpness of the main results"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages 95-99) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2023031267 |
| ISBN | 9781470461263 (paperback) |
| ISBN | (pdf) |