论文信息 - A zero-entropy mixing transformation whose product with itself is loosely Bernoulli

A zero-entropy mixing transformation whose product with itself is loosely Bernoulli

A zero-entropy mixing transformationT is constructed such thatT×T is loosely Bernoulli (LB). Previously known examples were not mixing. The construction is then generalized to yield a zero-entropy mixing transformationT such that then-fold productT × … ×T is LB for each positive integern. Furthermore, a flow with the same properties is obtained.

Marlies Gerber | Marlies Gerber

[1] M. Ratner. The cartesian square of the horocycle flow is not loosely Bernoulli , 1979 .

[2] J. Feldman. NewK-automorphisms and a problem of Kakutani , 1976 .

[3] D. Ornstein. Ergodic theory, randomness, and dynamical systems , 1974 .

[4] Benjamin Weiss,et al. Equivalence of measure preserving transformations , 1982 .

[5] M. Ratner. Horocycle flows are loosely Bernoulli , 1978 .

[6] E. A. Sataev. AN INVARIANT OF MONOTONE EQUIVALENCE DETERMINING THE QUOTIENTS OF AUTOMORPHISMS MONOTONELY EQUIVALENT TO A BERNOULLI SHIFT , 1977 .

[7] A. Rothstein. Versik processes: First steps , 1980 .

[8] Standardness of automorphisms of transposition of intervals and fluxes on surfaces , 1976 .

[9] A. Katok. MONOTONE EQUIVALENCE IN ERGODIC THEORY , 1977 .