On the Three-Legged Accessibility Property

Hertz, Jana Rodriguez; Ures, Raúl

doi:10.1007/978-3-030-16833-9_13

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…Se presentan propiedades dinámicas a través de derivada Schwarziana en [7]. En [11] y [14], se analizan conjuntos invariantes relevantes de dichos mapas.…”

Section: Introducción Y Antecedentesunclassified

Aspectos dinámicos del acoplamiento skew de la familia logística

Osuna,

Rojas-Milla

2023

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En este trabajo el objetivo fundamental es estudiar algunos aspectos de la evolución asintótica de las órbitas obtenidas por iterar el endomorfismo $$F_{\mu,\epsilon}(x,y)=( f_\mu(x), f_\mu(y)+\epsilon(x-y)),$$ donde $\mu >1$ es el parámetro de la familia logística: $ f_\mu(x)=\mu x(1-x)$ y $\epsilon>0,$ es el parámetro de acoplamiento. Este mapa biparam\'etrico es un híbrido entre dos clásicos en la teoría de los sistemas dinámicos, por un lado el paradigmático mapa cuadrático y por el otro el acoplamiento skew. El resultado principal será mostrar de manera detallada la construcción de un compacto invariante en el espacio de parámetros, junto con una descripción del comportamiento de las preimágenes de zonas en $ \mathbb R^2$ que juegan un rol importante en la comprensión de la dinámica del acoplamiento.

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“…Se presentan propiedades dinámicas a través de derivada Schwarziana en [7]. En [11] y [14], se analizan conjuntos invariantes relevantes de dichos mapas.…”

Section: Introducción Y Antecedentesunclassified

Aspectos dinámicos del acoplamiento skew de la familia logística

Osuna,

Rojas-Milla

2023

revint

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Robust minimality of strong foliations for DA diffeomorphisms: 𝑐𝑢-volume expansion and new examples

Hertz¹,

Ures²,

Yang³

2022

Trans. Amer. Math. Soc.

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Let f f be a C 2 C^2 partially hyperbolic diffeomorphisms of T 3 \mathbb {T}^3 (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism A A with eigenvalues λ s > 1 > λ c > λ u . \begin{equation*} \lambda _{s}>1>\lambda _{c}>\lambda _{u}. \end{equation*} Under the assumption that the set { x : ∣ log ⁡ det ( T f ∣ E c u ( x ) ) ∣≤ log ⁡ λ u } \begin{equation*} \{x: \,\mid \log \det (Tf\mid _{E^{cu}(x)})\mid \leq \log \lambda _{u} \} \end{equation*} has zero volume inside any unstable leaf of f f where E c u = E c ⊕ E u E^{cu} = E^c\oplus E^u is the center unstable bundle, we prove that the stable foliation of f f is C 1 C^1 robustly minimal, i.e., the stable foliation of any diffeomorphism C 1 C^1 sufficiently close to f f is minimal. In particular, f f is robustly transitive. We build, with this criterion, a new example of a C 1 C^1 open set of partially hyperbolic diffeomorphisms, for which the strong stable foliation and the strong unstable foliation are both minimal.

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Maximal entropy measures of diffeomorphisms of circle fiber bundles

Ures

Viana

Yang

2020

J. London Math. Soc.

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We characterize the maximal entropy measures of partially hyperbolic C 2 diffeomorphisms whose center foliations form circle bundles, by means of suitable finite sets of saddle points, that we call skeletons.In the special case of 3-dimensional nilmanifolds other than the torus, this entails the following dichotomy: either the diffeomorphism is a rotation extension of an Anosov diffeomorphismin which case there is a unique maximal measure, with full support and zero center Lyapunov exponents -or there exist exactly two ergodic maximal measures, both hyperbolic and whose center Lyapunov exponents have opposite signs. Moreover, the set of maximal measures varies continuously with the diffeomorphism.

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On the Three-Legged Accessibility Property

Cited by 3 publications

References 15 publications

Aspectos dinámicos del acoplamiento skew de la familia logística

Aspectos dinámicos del acoplamiento skew de la familia logística

Robust minimality of strong foliations for DA diffeomorphisms: 𝑐𝑢-volume expansion and new examples

Maximal entropy measures of diffeomorphisms of circle fiber bundles

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