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Spatial profile of the Majorana fermion wave function in a one-dimensional$p$-wave superconductors ($\cal{PWS}$) with quasi periodic disorder is shown toexhibit spatial oscillations. These oscillations damp out in the interior ofthe chain and are characterized by a period that has topological origin and isequal to the Chern number determining the Hall conductivity near half-fillingof a two-dimensional electron gas in a crystal. This mapping unfolds in view ofa correspondence between the critical point for the topological transition in$\cal{PWS}$ and the {\it strong coupling fixed point} of the Harper's equation.Oscillatory character of these modes persist in a generalized model related toan extended Harper system where the electrons also tunnel to the diagonals of asquare lattice. However, beyond a bicritical point, the Majorana oscillationsoccur with a random period, characterized by an invariant fractal set.

Topology Induced Oscillations in Majorana Fermions in a Quasiperiodic Superconducting Chain