On cusps and flat tops

Neil Dobbs[1]

  • [1] Department of Mathematics and Statistics PL 68 FIN-00014 University of Helsinki Finland

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 571-605
  • ISSN: 0373-0956

Abstract

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Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to C 1 + ϵ . The critical points are not required to verify a non-flatness condition, so the results are applicable to C 1 + ϵ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.

How to cite

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Dobbs, Neil. "On cusps and flat tops." Annales de l’institut Fourier 64.2 (2014): 571-605. <http://eudml.org/doc/275668>.

@article{Dobbs2014,
abstract = {Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to $C^\{1+\epsilon \}$. The critical points are not required to verify a non-flatness condition, so the results are applicable to $C^\{1+\epsilon \}$ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.},
affiliation = {Department of Mathematics and Statistics PL 68 FIN-00014 University of Helsinki Finland},
author = {Dobbs, Neil},
journal = {Annales de l’institut Fourier},
keywords = {Lyapunov exponent; Pesin theory; absolutely continuous invariant measures; interval dynamics; flat critical points},
language = {eng},
number = {2},
pages = {571-605},
publisher = {Association des Annales de l’institut Fourier},
title = {On cusps and flat tops},
url = {http://eudml.org/doc/275668},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Dobbs, Neil
TI - On cusps and flat tops
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 571
EP - 605
AB - Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to $C^{1+\epsilon }$. The critical points are not required to verify a non-flatness condition, so the results are applicable to $C^{1+\epsilon }$ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.
LA - eng
KW - Lyapunov exponent; Pesin theory; absolutely continuous invariant measures; interval dynamics; flat critical points
UR - http://eudml.org/doc/275668
ER -

References

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