Abstract
We developed a method for exactly determining the multiple inverses of quadratic planar maps. The quadratic planar map was transformed through an affine transformation into its conjugate domain, where all inverses can be exactly determined, and transform the inverses back. We showed that for all quadratic planar maps with non-vanishing critical curves, except for two exceptional cases of the map with a degenerate critical curve, there exists at least one available transformation. For both exceptional cases and for those maps with vanishing critical curves, the inverses are determinable without any transformation. This result can be applied to the calculation of stable manifolds of the quadratic planar map. It may help us further understand the dynamics, the basins of attraction, and the bifurcations associated with the quadratic planar map under iteration.
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