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Abstract:

Dimension conservation for almost every projection has been well-established by the work of Marstrand, Mattila and Hunt and Kaloshin. More recently, Hochman and Shmerkin used CP-chains, a tool first introduced by Furstenberg, to prove all projections preserve dimension of measures on [0,1]2 that are the product of a ×m-invariant and a ×n-invariant measure (for m, n multiplicatively independent). Using these tools, Ferguson, Fraser and Sahlsten extended that conservation result to (×m,×n)-invariant measures that are the push-forward of a Bernoulli scheme under the (m,n)-adic symbolic encoding. Their proof relied on a parametrization of conditional measures which could not be extended beyond the Bernoulli case. In this work, we extend their result from Bernoulli measures to Gibbs measures on any transitive SFT. Rather than attempt a similar parametrization, the proof is achieved by reducing the problem to that of the pointwise convergence of a double ergodic average which is known to hold when the system is exact. © 2016

Registro:

Documento: Artículo
Título:CP-chains and dimension preservation for projections of (×m,×n)-invariant Gibbs measures
Autor:Almarza, J.I.
Filiación:Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Int. Güiraldes 2160, Buenos Aires, Argentina
Palabras clave:Dynamical systems; Ergodicity; Fractal; Gibbs measures
Año:2017
Volumen:304
Página de inicio:227
Página de fin:265
DOI: http://dx.doi.org/10.1016/j.aim.2016.04.004
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v304_n_p227_Almarza

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Citas:

---------- APA ----------
(2017) . CP-chains and dimension preservation for projections of (×m,×n)-invariant Gibbs measures. Advances in Mathematics, 304, 227-265.
http://dx.doi.org/10.1016/j.aim.2016.04.004
---------- CHICAGO ----------
Almarza, J.I. "CP-chains and dimension preservation for projections of (×m,×n)-invariant Gibbs measures" . Advances in Mathematics 304 (2017) : 227-265.
http://dx.doi.org/10.1016/j.aim.2016.04.004
---------- MLA ----------
Almarza, J.I. "CP-chains and dimension preservation for projections of (×m,×n)-invariant Gibbs measures" . Advances in Mathematics, vol. 304, 2017, pp. 227-265.
http://dx.doi.org/10.1016/j.aim.2016.04.004
---------- VANCOUVER ----------
Almarza, J.I. CP-chains and dimension preservation for projections of (×m,×n)-invariant Gibbs measures. Adv. Math. 2017;304:227-265.
http://dx.doi.org/10.1016/j.aim.2016.04.004