Chaotic intermittency in maps with infinite derivative

ELASKAR, SERGIO; DEL RIO, EZEQUIEL; LORENZÓN, DENIS

Resistencia

Congreso; 2020 IEEE Congreso Bienal de Argentina, ARGENCON 2020 - 2020 IEEE Biennial Congress of Argentina, ARGENCON 2020; 2021

IEEE

The classical intermittency theory developed fortyyears ago considers a uniform reinjection probability densityfunction (RPD). However, in the last ten years, studies havefound a more general RPD, which depends on the type of pre-reinjection points, extreme or infinite derivative points. Recently,we have introduced an analytical scheme to estimate the non-uniform RPD when the pre-reinjection points are extreme. Here,this theoretical scheme is extended to embrace pre-reinjectionpoints with infinite derivative. The proposed theoretical method,to get the RPD, needs only the explicit expression of the map,and it is general and direct to use. For different intermittencytypes and different non-linearity, the theoretical predictions showa very high agreement with the numerical results.