We study the symplectic embedding capacity function for ellipsoids into dilates of polydisks as both and vary through . For , Frenkel and Müller showed that has an infinite staircase accumulating at , while for integer , Cristofaro-Gardiner, Frenkel and Schlenk found that no infinite staircase arises. We show that for arbitrary , the restriction of to is determined entirely by the obstructions from Frenkel and Müller’s work, leading on this interval to have a finite staircase with the number of steps tending to as . On the other hand, in contrast to the results of Cristofaro-Gardiner, Frenkel and Schlenk, for a certain doubly indexed sequence of irrational numbers we find that has an infinite staircase; these include both numbers that are arbitrarily large and numbers that are arbitrarily close to , with the corresponding accumulation points respectively arbitrarily large and arbitrarily close to .
"Infinite staircases in the symplectic embedding problem for four-dimensional ellipsoids into polydisks." Algebr. Geom. Topol. 19 (4) 1935 - 2022, 2019. https://doi.org/10.2140/agt.2019.19.1935