A characterization of uniquely ergodic interval exchange maps in terms of the Jacobi-Perron algorithm

Bauer, Max

doi:10.1007/bf01259355

Cited by 7 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By F we denote a map between M 0 F ol and Rng given by the formula F → A F . Notice, that F is correctly defined, since foliations with the unique measure have the convergent Jacobi-Perron fractions; this assertion follows from [Bauer 1996] [2]. [9].…”

Section: Af -Algebra Of Measured Foliationmentioning

confidence: 94%

See 1 more Smart Citation

AF-algebras and topology of mapping tori

Nikolaev

2015

Czech Math J

View full text Add to dashboard Cite

show abstract

Section: Af -Algebra Of Measured Foliationmentioning

confidence: 94%

“…Since ϕ preserves the leaves of F ϕ , one concludes that λ ′ i ∈ P (F ϕ ); therefore, λ ′ j = b ij λ i for a non-negative integer matrix B = (b ij ). According to [Bauer 1996] [2], the matrix B can be written as a finite product:…”

Section: Proof Of Lemmamentioning

confidence: 99%

AF-algebras and topology of mapping tori

Nikolaev

2015

Czech Math J

View full text Add to dashboard Cite

show abstract

“…where A, A ′ ∈ GL + n (Z) are the matrices, whose entries are non-negative integers. In view of the Proposition 3 of [1]:…”

Section: Modules and Continued Fractionsmentioning

confidence: 99%

“…. , θ n−1 ) is a vector with positive coordinates θ i = v (i+1) /v (1) . (Note that the θ i depend on a basis in the homology group; but a Z-module generated by the θ i does notsee lemma 1.)…”

Section: Introductionmentioning

confidence: 99%

Operator algebras and conjugacy problem for the pseudo-Anosov automorphisms of a surface

Nikolaev¹

2013

Pacific J. Math.

View full text Add to dashboard Cite

The conjugacy problem for the pseudo-Anosov automorphisms of a compact surface is studied. To each pseudo-Anosov automorphism φ, we assign an AF C * -algebra A φ (an operator algebra). It is proved that the assignment is functorial, i.e. every φ ′ , conjugate to φ, maps to an AF C * -algebra A φ ′ , which is stably isomorphic to A φ . The new invariants of the conjugacy of the pseudo-Anosov automorphisms are obtained from the known invariants of the stable isomorphisms of the AF C * -algebras. Namely, the main invariant is a triple (Λ, [I], K), where Λ is an order in the ring of integers in a real algebraic number field K and [I] an equivalence class of the ideals in Λ. The numerical invariants include the determinant ∆ and the signature Σ, which we compute for the case of the Anosov automorphisms. A question concerning the p-adic invariants of the pseudo-Anosov automorphism is formulated.

show abstract

“…Unlike the regular continued fraction algorithm, the JPA may diverge for certain vectors λ ∈ R n . However, for points of a generic subset of R n , the JPA converges [1]; in particular, the JPA for periodic fractions is always convergent.…”

Section: Preliminariesmentioning

confidence: 99%