scholarly journals Symbolic extension entropy: $c^r$ examples, products and flows

2006 ◽  
Vol 16 (2) ◽  
pp. 329-341 ◽  
Author(s):  
Mike Boyle ◽  
◽  
Tomasz Downarowicz ◽  
Keyword(s):  
Symbolic Extension

HURRICANES, CROPS, AND CAPITAL: THE METEOROLOGICAL INFRASTRUCTURE OF AMERICAN EMPIRE IN THE WEST INDIES

2016 ◽  
Vol 15 (4) ◽  
pp. 418-445 ◽  
Author(s):  
Jamie L. Pietruska
Keyword(s):  
West Indian ◽  
The United States ◽  
American Empire ◽  
The West ◽  
Knowledge Infrastructure ◽  
Military Security ◽  
Symbolic Extension ◽  
History Of ◽  
The Caribbean ◽  
Weather Service

This article examines the mutually reinforcing imperatives of government science, capitalism, and American empire through a history of the U.S. Weather Bureau's West Indian weather service at the turn of the twentieth century. The original impetus for expanding American meteorological infrastructure into the Caribbean in 1898 was to protect naval vessels from hurricanes, but what began as a measure of military security became, within a year, an instrument of economic expansion that extracted climatological data and produced agricultural reports for American investors. This article argues that the West Indian weather service was a project of imperial meteorology that sought to impose a rational scientific and bureaucratic order on a region that American officials considered racially and culturally inferior, yet relied on the labor of local observers and Cuban meteorological experts in order to do so. Weather reporting networks are examined as a material and symbolic extension of American technoscientific power into the Caribbean and as a knowledge infrastructure that linked the production of agricultural commodities in Cuba and Puerto Rico to the world of commodity exchange in the United States.

scholarly journals Symbolic dynamics for non-uniformly hyperbolic systems

2020 ◽  
pp. 1-68
Author(s):  
YURI LIMA
Keyword(s):  
Symbolic Dynamics ◽  
Hyperbolic Systems ◽  
Markov Partition ◽  
Equilibrium Measures ◽  
Markov Partitions ◽  
Recent Advances ◽  
Closed Orbits ◽  
Symbolic Extension ◽  
Uniformly Hyperbolic Systems

Abstract This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

scholarly journals Courtesan Singers as Courtiers: Power, Political Pawns, and the Arrest of virtuosa Nina Barcarola

2020 ◽  
Vol 73 (2) ◽  
pp. 207-267
Author(s):  
Amy Brosius
Keyword(s):  
Vocal Performance ◽  
The Public ◽  
Contemporary Politics ◽  
The Social ◽  
Archival Documents ◽  
Symbolic Extension ◽  
Male Dependents ◽  
The Public Sphere ◽  
And Gender ◽  
The City

This article gives a close reading of the “avvisi di Roma”—unpublished archival documents reporting on daily life in the city—that record the arrest in 1645 of famous Roman courtesan singer Nina Barcarola. Organized by the political enemies of Nina's main protector, Cardinal Antonio Barberini, the arrest was orchestrated so as to compromise the public honor of both. The reports of the arrest reflect a growing elite interest in female vocal performance in Rome, and attest to a rise in the social value of courtesan singers. Examining details provided in these reports, the article explores various aspects of Nina's life and courtesan singing culture more generally: the public honor and social practices of courtesan singers; the positive effect of singing on courtesan honor; the types of gatherings hosted by Nina; and her politically satirical public performances. It also analyzes Nina's relationship to various areas of contemporary politics—social, state, familial, and gender. The reports reveal that, in the public sphere, Nina, like Barberini's male dependents, served as a symbolic extension of the cardinal. By introducing courtesan singers—a significant, marginalized population—into musicological discourse on seventeenth-century Rome, the article broadens our understanding of Roman singing culture in this period.

scholarly journals A lower bound for topological entropy of generic non-Anosov symplectic diffeomorphisms

2013 ◽  
Vol 34 (5) ◽  
pp. 1503-1524 ◽  
Author(s):  
THIAGO CATALAN ◽  
ALI TAHZIBI
Keyword(s):  
Lyapunov Exponent ◽  
Lower Bound ◽  
Topological Entropy ◽  
Upper Semicontinuity ◽  
Periodic Points ◽  
Surface Diffeomorphisms ◽  
Symplectic Diffeomorphisms ◽  
Symbolic Extension ◽  
Symplectic Diffeomorphism ◽  
Volume Preserving

AbstractWe prove that a${C}^{1} $generic symplectic diffeomorphism is either Anosov or its topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of its periodic points. We also prove that${C}^{1} $generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension and, finally, we give examples of volume preserving surface diffeomorphisms which are not points of upper semicontinuity of the entropy function in the${C}^{1} $topology.

scholarly journals A faithful symbolic extension

2012 ◽  
Vol 11 (3) ◽  
pp. 1051-1062 ◽  
Author(s):  
Jacek Serafin ◽  
Keyword(s):  
Symbolic Extension

scholarly journals Zero-dimensional and symbolic extensions of topological flows

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Burguet ◽  
Ruxi Shi
Keyword(s):  
Suspension Flow ◽  
Dimensional System ◽  
Orbit Equivalence ◽  
Suspension Flows ◽  
Dimensional Flow ◽  
Symbolic Extension ◽  
Zero Sequence ◽  
Full Shift ◽  
Symbolic Flow ◽  
Roof Function

<p style='text-indent:20px;'>A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a zero-dimensional flow. Following [<xref ref-type="bibr" rid="b6">6</xref>] we deduce that any topological flow admits an extension by a symbolic flow if and only if its time-<inline-formula><tex-math id="M1">\begin{document}$ t $\end{document}</tex-math></inline-formula> map admits an extension by a subshift for any <inline-formula><tex-math id="M2">\begin{document}$ t\neq 0 $\end{document}</tex-math></inline-formula>. Moreover the existence of such an extension is preserved under orbit equivalence for regular topological flows, but this property does not hold for singular flows. Finally we investigate symbolic extensions for singular suspension flows. In particular, the suspension flow over the full shift on <inline-formula><tex-math id="M3">\begin{document}$ \{0,1\}^{\mathbb Z} $\end{document}</tex-math></inline-formula> with a roof function <inline-formula><tex-math id="M4">\begin{document}$ f $\end{document}</tex-math></inline-formula> vanishing at the zero sequence <inline-formula><tex-math id="M5">\begin{document}$ 0^\infty $\end{document}</tex-math></inline-formula> admits a principal symbolic extension or not depending on the smoothness of <inline-formula><tex-math id="M6">\begin{document}$ f $\end{document}</tex-math></inline-formula> at <inline-formula><tex-math id="M7">\begin{document}$ 0^\infty $\end{document}</tex-math></inline-formula>.</p>

Symbolic Extension and Its Corruption of Music

1981 ◽  
Vol 20 (1/2) ◽  
pp. 331 ◽  
Author(s):  
Barton McLean
Keyword(s):  
Symbolic Extension

Modeling potential as fiber entropy and pressure as entropy

2014 ◽  
Vol 35 (4) ◽  
pp. 1165-1186 ◽  
Author(s):  
TOMASZ DOWNAROWICZ ◽  
GUO HUA ZHANG
Keyword(s):  
Dynamical System ◽  
Variational Principle ◽  
Topological Pressure ◽  
Extended System ◽  
Additional Information ◽  
Upper Semicontinuous ◽  
Monotonicity Assumption ◽  
Symbolic Extension ◽  
Natural Information ◽  
New Interpretation

AbstractWe first prove that topological fiber entropy potential in a relatively symbolic extension (topological joining with a subshift) of a topological dynamical system (which is a non-negative, non-decreasing, upper semicontinuous and subadditive potential$\mathfrak{H}$) yields topological pressure equal to the topological entropy of the extended system. The terms occurring on the other side of the variational principle for pressure are equal to the extension entropies of the invariant measures. Thus the variational principle for pressure reduces to the usual variational principle (for entropy) applied to the extended system. Next we prove our main theorem saying that every non-negative, upper semicontinuous and subadditive potential$\mathfrak{F}$(we drop the monotonicity assumption) is ‘nearly equal’ to the fiber entropy potentialHin some relatively symbolic extension of the system, in the sense that all terms occurring in the variational principle for pressure are the same for both potentials. This gives a new interpretation of all such potentials$\mathfrak{F}$as a kind of additional information function enhancing the natural information arising from the dynamical system, and provides a new proof of the variational principle for pressure. At the end of the paper we provide examples showing that both assumptions, continuity and additivity, under which so-called lower pressure (defined with the help of spanning sets) equals the pressure, are essential, already in the class of non-negative, upper semicontinuous, subadditive potentials.

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