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The spectrum of dynamical systems arising from substitutions of constant length

1978
*
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
*

A lar ge class

doi:10.1007/bf00534241
fatcat:xbgqpvqwdbe7rje55vctuxj6ga
*of*examples*of**minimal**flows*are given by those*arising**from**substitutions*. ... An interesting side result is that if (X,T,y) is a dyna mical system*arising**from*a*substitution**of**constant**length*then T n is*minimal*if and only if T n is ergodic. ... J>iJ Ui- According to theorem 1 (X(e),T) is topologically isomorphic to a*substitution**flow**of**constant**length*if X 2 = 0 . We conjecture that this condition is also necessary. ...##
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Mixing properties of substitutions

1978
*
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
*

We show that the

doi:10.1007/bf00534205
fatcat:xzteegizjfh2hdk7b6yahjyaa4
*minimal**flow*(X, T)*arising**from*n is topologically strongly mixing*of*order two, but not*of*order three, pro viding the first example*of*a*minimal**flow*with these properties. ... (If*minimality*is not required, an example can be found in [6] .) It is also proved that no*minimal**flow**arising**from*a*substitution*can be topologically strongly mixing*of*all orders. ...##
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Page 422 of Mathematical Reviews Vol. 44, Issue 2
[page]

1972
*
Mathematical Reviews
*

The authors examine the structure

*of**constant**length**substitution**minimal*sets in the bilateral 2-shift (Q, ¢), i.e.,*minimal*sets*arising**from*a*substitution**of*the form 6(0)=aga,, ---, 4,1, (1) =bob, ... It is | shown by spectral considerations that*minimal*sets*arising**from*continuous*substitutions*are never isomorphic to those*from*discrete*substitutions*. ...##
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Page 1689 of Mathematical Reviews Vol. 45, Issue 6
[page]

1973
*
Mathematical Reviews
*

This paper is devoted to an extensive and rather deep study

*of**substitution**minimal*sets (M,c)*of**constant**length*, i.e.,*minimal*sets*of*the symbolic*flow*on n symbols that*arise**from*a map*of*the form ... 0(i)=2,%,---x,, where 0sisn—-1, 0S2,<Sn-—1, and the*length*r is*constant*for each i. ...##
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Substitutions, tiling dynamical systems and minimal self-joinings
[article]

2014
*
arXiv
*
pre-print

We show that the

arXiv:1402.5672v1
fatcat:lnduawthgnegtcqvclsudxz7la
*substitution*subshifts*arising**from*\theta and \eta have*minimal*self-joinings and are mildly mixing. ... We also give a criterion for 1-dimensional tiling systems*arising**from*\theta or \eta to have*minimal*self-joinings. We apply this to obtain examples*of*mildly mixing 1-dimensional tiling systems. ... Let ζ be an aperiodic, primitive,*constant**length**substitution*on the alphabet A = {0, 1}, where the number*of*0s occurring in ζ(0) is different*from*the number*of*0s occurring in ζ(1). ...##
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Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type

2002
*
Canadian mathematical bulletin
*

*flow*. ... As a corollary, we prove pure discrete spectrum for every R-action associated with a two-symbol

*substitution*

*of*Pisot type (this is conjectured for an arbitrary number

*of*symbols). ... The

*substitution*ζ is said to have

*constant*

*length*if i → |ζ(i)| is

*constant*on A; otherwise, it has

*non*-

*constant*

*length*. Definition. ...

##
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A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds

2011
*
Journal of the Acoustical Society of America
*

A theoretical

doi:10.1121/1.3586785
pmid:21786907
fatcat:ljlxpnlm3ja6tblbmwfkrkb264
*flow*solution is presented for predicting the pressure distribution along the vocal fold walls*arising**from*asymmetric*flow*that forms during the closing phases*of*speech. ... The method was validated with experimental velocity data*from*7.5 times life-size vocal fold models, acquired for varying*flow*rates and glottal divergence angles. ... ACKNOWLEDGMENTS This work was supported by a grant*from*the National Science Foundation (CBET 0828903). ...##
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Flow views and infinite interval exchange transformations for recognizable substitutions
[article]

2021
*
arXiv
*
pre-print

As an example

arXiv:2103.07997v3
fatcat:u3vkd22opvbz5ouvf75d3tawve
*of*utility, some spectral results for*constant*-*length**substitutions*are included. ... A*flow*view is the graph*of*a measurable conjugacy between a*substitution*or S-adic subshift and an exchange*of*infinitely many intervals (IIET) in [0,1]. ... Since µ(E δ ) = m(D δ ), this contradicts the definition*of*D δ and completes the proof. 5.4. Pictures for the*non*-*constant**length*case. ...##
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A general model for metabolic scaling in self-similar asymmetric networks

2017
*
PLoS Computational Biology
*

Biological allometries, such as metabolic scaling, have been hypothesized to result

doi:10.1371/journal.pcbi.1005394
pmid:28319153
pmcid:PMC5378416
fatcat:e3nc4yorare5fpu3in7n4q2yku
*from*selection to maximize how vascular networks fill space yet*minimize*internal transport distances and resistances ... Our work shows how space-filling and fluid*flow*principles constrain allowed branching morphologies within the context*of*our model. ... Acknowledgments The authors wish to thank Alex Cronin, Drew Milsom, and Elif Tekin for their assistance in editing early versions*of*the manuscript, the Santa Fe Institute for hosting the authors, and ...##
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On an integrable magnetic geodesic flow on the two-torus
[article]

2016
*
arXiv
*
pre-print

We completely integrate the magnetic geodesic

arXiv:1508.03745v2
fatcat:bg22lobzb5fszp5icdvuv6sydu
*flow*on a flat two-torus with the magnetic field F = cos (x) dx ∧ dy and describe all contractible periodic magnetic geodesics. ... However the*lengths**of*noncontractible contours are at least √ 2E 2π, i.e., the*length**of*γ +− and*of*γ −+ which are*minimal**non*-contractible geodesics on T 2 . ... Theorems 2 and 3 say that the*flow*in study supplies an explicit example*of*such a situation. Actually this article*arises*as an answer to the question by A. ...##
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The effect of confining boundaries on viscous gravity currents

2007
*
Journal of Fluid Mechanics
*

Similarity solutions are obtained

doi:10.1017/s0022112007005174
fatcat:daeossho65c7tmapujq342ugzm
*from*the governing mathematical equations and compared with closely matching data*from*laboratory experiments in which the propagation*of*glycerine along different channels ... Geological applications*of*the results are discussed briefly. ... These results are only valid for the instantaneous release*of*a fixed volume*of*viscous fluid. Additional relationships will*arise*if the discharge rate is not*constant*. ...##
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Self-similarity and spectral theory: on the spectrum of substitutions
[article]

2021
*
arXiv
*
pre-print

In this survey

arXiv:2111.01109v2
fatcat:apzci5lcrfhf3o3z2qctmqcchu
*of*the spectral properties*of**substitution*dynamical systems we consider primitive aperiodic*substitutions*and associated dynamical systems: ℤ-actions and ℝ-actions, the latter viewed as ... tiling*flows*. ...*Substitutions**of**non*-*constant**length*. ...##
###
Induced airflow in flying insects I. A theoretical model of the induced flow

2006
*
Journal of Experimental Biology
*

In this analysis, I adopt Ellington's method and represent c(r) using Beta functions appropriately rescaled with a

doi:10.1242/jeb.01957
pmid:16354776
fatcat:dbnwvvxpcfdlbf6j2bl5wahdm4
*constant**non*-dimensional parameter B i , the ratio*of*maximum*non*-dimensional chord*length*... List*of*symbols A area*of*actuator disk AR aspect ratio B i chord rescale ratio c mean chord*length*c(r) chord*length*as a function*of*radial position c(r)*non*-dimensional chord*length*C L lift coefficient ...##
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Page 197 of Mathematical Reviews Vol. 57, Issue 1
[page]

1979
*
Mathematical Reviews
*

Japan ily

*of*24 (1972), 285-306; MR 45 #2688] with certain restrictions on 0.) r such The author also considers*substitutions**of**non*-*constant**length*. on*of*| For such a*substitution*@ on r symbols {0, ... The author shows that if (/,, ---,/,_,) is a right eigenvector*of*the no. 5, | matrix (/,,), then (X(4), T) is topologically isomorphic to a mini- rnaul) mal set*arising**from*a*substitution**of**constant*...##
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Optical flow: a curve evolution approach

1996
*
IEEE Transactions on Image Processing
*

A novel approach for the computation

doi:10.1109/83.491336
pmid:18285148
fatcat:5w5gdfxh3baxjngntejxzhj77i
*of*optical*flow*based on an L1 type*minimization*is presented. ... A numerical approach based on computation*of*evolving curves is proposed for computing the optical*flow*field and results*of*experiments are presented. ... The level set is given as fIf(x(s), y(s)) = IC =*constant*. (2.10) Differentiating twice, solving for the various derivatives w.r.t the arc-*length*and then simply*substituting*in: ( 2.11) we may write ...
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