Bifurcation to badly ordered orbits in one-parameter families of circle maps, or angels fallen from the devil’s staircase
Bifurcation to badly ordered orbits in one-parameter families of circle maps, or angels fallen from the devil’s staircase
We discuss the structure of the bifurcation set of a one-parameter family of endomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{S^1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> having two critical points and negative Schwarzian derivative. We concentrate on the case in …