For almost every tent map, the turning point is typical

• Autorzy: Henk Bruin
• Języki publikacji: EN

Abstrakty

EN

Let $T_a$ be the tent map with slope a. Let c be its turning point, and $μ_a$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, $ʃ g dμ_a = lim_{n → ∞} \frac1n ∑_{i=0}^{n-1} g(T^i_a(c))$. As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.

Kategorie tematyczne

• 28D20: Entropy and other invariants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 3
• Strony: 215-235

Daty

wydano

1998

otrzymano

1996-08-12

poprawiono

1997-05-15

Twórcy

autor

Henk Bruin

• KTH, Department of Mathematics, 100 44 Stockholm, Sweden,

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