×

Invariant measures for interval maps with different one-sided critical orders. (English) Zbl 1355.37059

Summary: For an interval map whose critical point set may contain critical points with different one-sided critical orders and jump discontinuities, under a mild condition on critical orbits, we prove that it has an invariant probability measure which is absolutely continuous with respect to Lebesgue measure by using the methods of H. Bruin et al. [Invent. Math. 172, No. 3, 509–533 (2008; Zbl 1138.37019)], together with ideas from T. Nowicki and S. van Strien [Invent. Math. 105, No. 1, 123–136 (1991; Zbl 0736.58030)]. We also show that it admits no wandering intervals.

MSC:

37E05 Dynamical systems involving maps of the interval
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1017/S0143385700001802 · Zbl 0532.28014 · doi:10.1017/S0143385700001802
[2] DOI: 10.1007/978-3-642-78043-1 · doi:10.1007/978-3-642-78043-1
[3] DOI: 10.1007/s00222-007-0108-4 · Zbl 1138.37019 · doi:10.1007/s00222-007-0108-4
[4] DOI: 10.1007/BF02698845 · Zbl 0703.58030 · doi:10.1007/BF02698845
[5] DOI: 10.1016/j.aim.2009.03.004 · Zbl 1184.37032 · doi:10.1016/j.aim.2009.03.004
[6] DOI: 10.3934/dcds.2010.27.557 · Zbl 1214.37035 · doi:10.3934/dcds.2010.27.557
[7] DOI: 10.1007/BF01237679 · Zbl 0797.58051 · doi:10.1007/BF01237679
[8] DOI: 10.1017/S0143385706000629 · Zbl 1110.37037 · doi:10.1017/S0143385706000629
[9] DOI: 10.1007/BF01232258 · Zbl 0736.58030 · doi:10.1007/BF01232258
[10] DOI: 10.1007/BF02698686 · Zbl 0477.58020 · doi:10.1007/BF02698686
[11] DOI: 10.1016/S0294-1449(00)00111-6 · Zbl 0983.37022 · doi:10.1016/S0294-1449(00)00111-6
[12] DOI: 10.1017/S0143385700007902 · Zbl 0809.58026 · doi:10.1017/S0143385700007902
[13] DOI: 10.1007/BF01217727 · Zbl 0583.58016 · doi:10.1007/BF01217727
[14] DOI: 10.1016/S1874-575X(06)80028-7 · doi:10.1016/S1874-575X(06)80028-7
[15] DOI: 10.1007/978-1-4612-4286-4 · doi:10.1007/978-1-4612-4286-4
[16] Dunford, Linear Operators. Part I: General Theory (1957)
[17] DOI: 10.1007/s00220-003-0928-z · Zbl 1098.37034 · doi:10.1007/s00220-003-0928-z
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.