Symmetric S-unimodal mappings and positive Liapunov exponents
T Nowicki - Ergodic Theory and Dynamical Systems, 1985 - cambridge.org
Ergodic Theory and Dynamical Systems, 1985•cambridge.org
… Symmetric S-unimodal functions with positive Liapunov exponent of the critical value
have an invariant measure absolutely continuous with respect to Lebesgue measure. …
Collet and Eckmann [3] proved the existence of such a measure for S-unimodal mappings
which (apart from some weak regularity assumptions) satisfy the two following conditions: …
By symmetry we have |cn-(b')n|<|c-fe'| and (c, b') satisfies *(n). Since bn = (b')n = c we have
either/"(c, b)<= (c, b) or/"(c, fe')c(c, ft')Hence / has a sink which contradicts lemma 2. …
have an invariant measure absolutely continuous with respect to Lebesgue measure. …
Collet and Eckmann [3] proved the existence of such a measure for S-unimodal mappings
which (apart from some weak regularity assumptions) satisfy the two following conditions: …
By symmetry we have |cn-(b')n|<|c-fe'| and (c, b') satisfies *(n). Since bn = (b')n = c we have
either/"(c, b)<= (c, b) or/"(c, fe')c(c, ft')Hence / has a sink which contradicts lemma 2. …
Symmetric S-unimodal functions with positive Liapunov exponent of the critical value have an invariant measure absolutely continuous with respect to Lebesgue measure.
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