Abstract
We prove the ergodicity for the discontinuous sawtooth map, adapting a technique previously used in billiard theory. The core of the proof is the construction of a Hopf chain passing through a countable dense set of discontinuity lines.
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Vaienti, S. Ergodic properties of the discontinuous sawtooth map. J Stat Phys 67, 251–269 (1992). https://doi.org/10.1007/BF01049033
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DOI: https://doi.org/10.1007/BF01049033