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Banach
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If $f$ is piecewise $C^2$, since your map is piecewise expanding it has an ACIM. See Lasota and York (Trans AMS, 1973).

See also the Chaos, Fractals, and Noise by A. Lasota and M. Mackey. One of the theorems in Ch. 6 might work for your maps.

If $f$ is piecewise $C^2$, since your map is piecewise expanding it has an ACIM. See Lasota and York (Trans AMS, 1973).

If $f$ is piecewise $C^2$, since your map is piecewise expanding it has an ACIM. See Lasota and York (Trans AMS, 1973).

See also the Chaos, Fractals, and Noise by A. Lasota and M. Mackey. One of the theorems in Ch. 6 might work for your maps.

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Banach
Banach
  • 29
  • 2
  • 5

If $f$ is piecewise $C^2$, since your map is piecewise expanding it has an ACIM. See Lasota and York (Trans AMS, 1973).