<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Christopher G. Pinner</style></author><author><style face="normal" font="default" size="100%">Dan Wolczuk</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the Inhomogeneous Hall&amp;#39;s Ray of Period-One Quadratics</style></title><secondary-title><style face="normal" font="default" size="100%">Experimental Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2001</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://projecteuclid.org/euclid.em/1069855248</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">10</style></volume><pages><style face="normal" font="default" size="100%">487-496</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
	For quadratics with period-one negative continued fraction expansions,
&lt;/p&gt;

&lt;p align=&quot;center&quot;&gt;
	X\theta =\frac{1}{ a-{\dfrac{\mathstrut 1}{a-{\dfrac{\mathstrut 1}{a- \cdots }}}}},
&lt;/p&gt;

&lt;p&gt;
	we show that the inhomogeneous Lagrange spectrum,
&lt;/p&gt;

&lt;p align=&quot;center&quot;&gt;
	\bL (\theta) :=\bigl\{ \liminf\nolimits_{|n|\rightarrow \infty} |n|@\|n\theta -\gamma\| : \gamma \in \funnyR,\; \gamma \not\in \funnyZ+\theta \funnyZ\bigr\},
&lt;/p&gt;

&lt;p&gt;
	contains an inhomogeneous Hall's ray &lt;span class=&quot;MathJax&quot; data-mathml=&quot;&lt;math xmlns=&amp;quot;http://www.w3.org/1998/Math/MathML&amp;quot;&gt;&lt;mo stretchy=&amp;quot;false&amp;quot;&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo stretchy=&amp;quot;false&amp;quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;amp;#x03B8;&lt;/mi&gt;&lt;mo stretchy=&amp;quot;false&amp;quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&amp;quot;false&amp;quot;&gt;]&lt;/mo&gt;&lt;/math&gt;&quot; id=&quot;MathJax-Element-1-Frame&quot; role=&quot;presentation&quot; style=&quot;position:relative;&quot; tabindex=&quot;0&quot;&gt;&lt;nobr aria-hidden=&quot;true&quot;&gt;&lt;span class=&quot;math&quot; id=&quot;MathJax-Span-1&quot; style=&quot;width:3.812em;display:inline-block;&quot;&gt;&lt;span style=&quot;display:inline-block;position:relative;width:3.155em;height:0px;120%;&quot;&gt;&lt;span style=&quot;position:absolute;clip:rect(1.393em,1003.04em,2.75em,-1000em);top:-2.321em;left:0em;&quot;&gt;&lt;span class=&quot;mrow&quot; id=&quot;MathJax-Span-2&quot;&gt;&lt;span class=&quot;mo&quot; id=&quot;MathJax-Span-3&quot; style=&quot;MathJax_Main;&quot;&gt;[&lt;/span&gt;&lt;span class=&quot;mn&quot; id=&quot;MathJax-Span-4&quot; style=&quot;MathJax_Main;&quot;&gt;0&lt;/span&gt;&lt;span class=&quot;mo&quot; id=&quot;MathJax-Span-5&quot; style=&quot;MathJax_Main;&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;mi&quot; id=&quot;MathJax-Span-6&quot; style=&quot;MathJax_Math;font-style:italic;padding-left:0.167em;&quot;&gt;c&lt;/span&gt;&lt;span class=&quot;mo&quot; id=&quot;MathJax-Span-7&quot; style=&quot;MathJax_Main;&quot;&gt;(&lt;/span&gt;&lt;span class=&quot;mi&quot; id=&quot;MathJax-Span-8&quot; style=&quot;MathJax_Math;font-style:italic;&quot;&gt;θ&lt;/span&gt;&lt;span class=&quot;mo&quot; id=&quot;MathJax-Span-9&quot; style=&quot;MathJax_Main;&quot;&gt;)&lt;/span&gt;&lt;span class=&quot;mo&quot; id=&quot;MathJax-Span-10&quot; style=&quot;MathJax_Main;&quot;&gt;]&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/nobr&gt;&lt;/span&gt;
&lt;/p&gt;

&lt;p&gt;
	with $$c(\theta)=\tfrac{1}{4}\bigl(1-O(a^{-1/2})\bigr)\hbox{.}
&lt;/p&gt;

&lt;p&gt;
	We describe gaps in the spectrum showing that this is essentially best possible. Pictures of computed spectra are included. Investigating such pictures led us to these results.
&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue></record></records></xml>