Local dynamics of planar maps with a non-isolated fixed point exhibiting 1–1 resonance

Abstract

Abstract We give a complete classification of all possible dynamical behavior scenarios valid in a neighborhood of non-isolated 1–1 resonant fixed points for planar maps that are real analytic. Examples from the literature are discussed.

Keywords

• Planar difference equation
• Planar map
• 1–1 resonance
• Non-hyperbolic fixed point
• Local behavior