Disorder and topology compete in one-dimensional systems, yet analytical results beyond perturbative limits remain scarce. We derive a nonperturbative, energy-dependent expression for the Lyapunov exponent of the disordered Su-Schrieffer-Heeger (SSH) chain in the presence of both on-site and hopping disorder. Our approach is based on a closed recurrence relation for the local density whose disorder average yields an effective transfer problem at the unit-cell level. The resulting energy-dependent Lyapunov exponent quantitatively matches numerical results across a broad range of disorder strengths and hopping asymmetries. We find that the magnitude of the Lyapunov exponent is independent of the topological phase for a semi-infinite chain. We further compute the real-space winding number under disorder and show the contrasting roles of hopping disorder and on-site disorder in the stability of the topological phase.

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• Localization
• Quantum phase transitions
• Symmetry protected topological states
• Topological insulators
• Su-Schrieffer-Heeger model