Symmetric periodic Reeb orbits on the sphere
Symmetric periodic Reeb orbits on the sphere
A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript 2 n plus 1"> <mml:semantics> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">S^{2n+1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has at least <inline-formula content-type="math/mathml"> <mml:math …