An alternative approach to generalised BV  and the application to  expanding interval maps

Oliver Butterley

doi:10.3934/dcds.2013.33.3355

Article Contents

2013, Volume 33, Issue 8: 3355-3363. Doi: 10.3934/dcds.2013.33.3355

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An alternative approach to generalised BV and the application to expanding interval maps

Oliver Butterley^1,

1.
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientica, 00133 Roma

Received: April 2012

Revised: May 2012

Published: August 2013

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Abstract

We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where the weighting used in the transfer operator is not better than piecewise Hölder continuous and the partition on which the map is continuous may possess a countable number of elements. For such weighted transfer operators we give upper bounds for both the spectral radius and for the essential spectral radius.

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Mathematics Subject Classification: 37E05, 37A25.

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References

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