Non-uniqueness for specifications in $\ell ^{2+\unicode[STIX]{x1D716}}$
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DOI: 10.1017/etds.2016.101
Abstract: For every $p>2$ , we construct a regular and continuous specification ( $g$ -function), which has a variation sequence that is in $\ell ^{p}$ and which admits multiple Gibbs measures. Combined with a result of… read more here.
Keywords: non uniqueness; ell unicode; specifications ell; stix x1d716 ... See more keywords
Surjunctivity and topological rigidity of algebraic dynamical systems
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DOI: 10.1017/etds.2017.41
Abstract: Let $X$ be a compact metrizable group and let $\unicode[STIX]{x1D6E4}$ be a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,\unicode[STIX]{x1D6E4})$ is surjunctive, i.e. every… read more here.
Keywords: stix x1d6e4; topological rigidity; systems surjunctivity; dynamical systems ... See more keywords
Relative equilibrium states and class degree
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DOI: 10.1017/etds.2017.50
Abstract: Given a factor code $\unicode[STIX]{x1D70B}$ from a shift of finite type $X$ onto a sofic shift $Y$ , an ergodic measure $\unicode[STIX]{x1D708}$ on $Y$ , and a function $V$ on $X$ with sufficient regularity, we… read more here.
Keywords: stix; unicode stix; class degree; stix x1d708 ... See more keywords
Shy shadows of infinite-dimensional partially hyperbolic invariant sets
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DOI: 10.1017/etds.2017.65
Abstract: Let ${\mathcal{R}}$ be a strongly compact $C^{2}$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_{F}{\mathcal{R}}$ is dense for every $F$ . Let $\unicode[STIX]{x1D6FA}$ be… read more here.
Keywords: stix; stix x1d6ff; unicode stix; stix x1d6fa ... See more keywords
Integrality properties of Böttcher coordinates for one-dimensional superattracting germs
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DOI: 10.1017/etds.2018.41
Abstract: Let $R$ be a ring of characteristic $0$ with field of fractions $K$ and let $m\geq 2$ . The Böttcher coordinate of a power series $\unicode[STIX]{x1D711}(x)\in x^{m}+x^{m+1}R\unicode[STIX]{x27E6}x\unicode[STIX]{x27E7}$ is the unique power series $f_{\unicode[STIX]{x1D711}}(x)\in x+x^{2}K\unicode[STIX]{x27E6}x\unicode[STIX]{x27E7}$ satisfying… read more here.
Keywords: stix x1d711; unicode stix; x1d711 unicode; unicode ... See more keywords
Pointwise equidistribution and translates of measures on homogeneous spaces
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DOI: 10.1017/etds.2018.44
Abstract: Let $(X,\mathfrak{B},\unicode[STIX]{x1D707})$ be a Borel probability space. Let $T_{n}:X\rightarrow X$ be a sequence of continuous transformations on $X$ . Let $\unicode[STIX]{x1D708}$ be a probability measure on $X$ such that $(1/N)\sum _{n=1}^{N}(T_{n})_{\ast }\unicode[STIX]{x1D708}\rightarrow \unicode[STIX]{x1D707}$ in the… read more here.
Keywords: stix x1d708; homogeneous spaces; equidistribution; unicode stix ... See more keywords
A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions
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DOI: 10.1017/etds.2018.51
Abstract: Over the last few years Pohl (partly jointly with coauthors) has developed dual ‘slow/fast’ transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces $\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$ with… read more here.
Keywords: stix x1d6e4; zeta functions; selberg zeta; stix ... See more keywords
A new mean ergodic theorem for tori and recurrences
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DOI: 10.1017/etds.2019.70
Abstract: Let $X$ be a finite-dimensional connected compact abelian group equipped with the normalized Haar measure $\unicode[STIX]{x1D707}$ . We obtain the following mean ergodic theorem over ‘thin’ phase sets. Fix $k\geq 1$ and, for every $n\geq… read more here.
Keywords: stix; ergodic theorem; mean ergodic; unicode stix ... See more keywords
HIGHER RANDOMNESS AND GENERICITY
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DOI: 10.1017/fms.2017.27
Abstract: We use concepts of continuous higher randomness, developed in Bienvenu et al. [‘Continuous higher randomness’, J. Math. Log. 17(1) (2017).], to investigate $\unicode[STIX]{x1D6F1}_{1}^{1}$ -randomness. We discuss lowness for $\unicode[STIX]{x1D6F1}_{1}^{1}$ -randomness, cupping with $\unicode[STIX]{x1D6F1}_{1}^{1}$ -random sequences,… read more here.
Keywords: stix x1d6f1; higher randomness; randomness; randomness genericity ... See more keywords
HIGH ORDER PARACONTROLLED CALCULUS
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DOI: 10.1017/fms.2019.44
Abstract: We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm a whole class of singular partial differential equations with the same efficiency as regularity structures. This… read more here.
Keywords: paracontrolled calculus; order paracontrolled; stix x2202; high order ... See more keywords
All-optical $\unicode[STIX]{x1D707}^{-}$ acceleration in the laser wakefield
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DOI: 10.1017/hpl.2018.65
Abstract: Muons produced by the Bethe–Heitler process from laser wakefield accelerated electrons interacting with high $Z$ materials have velocities close to the laser wakefield. It is possible to accelerate those muons with laser wakefield directly. Therefore… read more here.
Keywords: laser; energy; acceleration; laser wakefield ... See more keywords