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We identify contact transformations which linearize the given equations inthe Riccati and Abel chains of nonlinear scalar and coupled ordinarydifferential equations to the same order. The identified contacttransformations are not of Cole-Hopf type and are \emph {new} to theliterature. The linearization of Abel chain of equations is also demonstratedexplicitly for the first time. The contact transformations can be utilized toderive dynamical symmetries of the associated nonlinear ODEs. The widerapplicability of identifying this type of contact transformations and themethod of deriving dynamical symmetries by using them is illustrated throughtwo dimensional generalizations of the Riccati and Abel chains as well.

Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains