Abstract
We consider reversible dynamical systems with a fixed point which is also fixed under the reversing involution; we show that applying to such a system the canonical Poincaré-Dulac procedure reducing a dynamical system to its normal form, we obtain a normal form which is still reversible (under the same involution as the original system); conversely, we also show how to obtain all the reversible systems which are reduced to a given reversible form. This allows one to (locally) classify reversible dynamical systems, and reduce their (local) study to that of reversible normal forms.
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Gaeta, G. Normal forms of reversible dynamical systems. Int J Theor Phys 33, 1917–1928 (1994). https://doi.org/10.1007/BF00671033
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DOI: https://doi.org/10.1007/BF00671033