Horseshoe in a class of planar mappings (Q2491479)

Summary: Bursting dynamics of mappings is investigated in this paper. We first present stability analysis of the mappings' equilibria with various parameters. Then, for three mappings \(P\), \(\bar{P}\), and \(\widehat{P}\) with different parameters, we study their powers \(P^4\), \(\bar{P}^6\), and \(\widehat{P}^4\). We show that the mappings thus obtained are chaotic by giving a rigorous verification of existence of horseshoes in these mappings. Precisely, we prove that the mapping \(\bar{P}^6\) is semiconjugate to the 3-shift mapping; the mappings \(P^4\) and \(\widehat{P}^4\) are semiconjugate to the 4-shift mapping.