Examples of Retarded Functional Differential Equations on Manifolds

Autonomous retarded functional differential equations on ℝⁿ are usually defined as equations of the form where f maps C⁰(I, ℝⁿ) into ℝⁿ. Taking M = ℝⁿ and identifying TM with ℝⁿ × ℝⁿ, one can define the function F: C⁰(I,M) → TM such that F(φ) = φ (0), f(φ)). If f is continuous, then F is an RFDE on M = ℝⁿ which can be identified with the above equation.