000164176 001__ 164176 000164176 005__ 20251127172930.0 000164176 0247_ $$2doi$$a10.1016/j.physd.2025.135036 000164176 0248_ $$2sideral$$a146333 000164176 037__ $$aART-2025-146333 000164176 041__ $$aeng 000164176 100__ $$aChacón, Ricardo 000164176 245__ $$aOn some elliptic generalizations of the Metropolis–Stein–Stein map 000164176 260__ $$c2025 000164176 5060_ $$aAccess copy available to the general public$$fUnrestricted 000164176 5203_ $$aJacobian elliptic functions have been at the heart of nonlinear science for two hundred years. Through the exploration of two biparametric (,) elliptic-based generalizations of the Metropolis–Stein–Stein (MSS) map, +1 = sn() and +1 = sncn(), with sn and cn being Jacobian elliptic functions of parameter , we provide analytical and numerical evidence that solely varying the impulse per unit of amplitude of the periodic map functions, while keeping its amplitude constant, shifts the bifurcation amplitudes, including those corresponding to the onset and extinction of chaos, with respect to the case of the standard MSS map. The analyses of the Schwarzian derivative of the two elliptic maps indicate that a change of its sign from negative to positive as the shape parameter is increased from 0 to 1 only occurs for the map sncn, while the corresponding routes order↔chaos for both elliptic maps still follow Feigenbaum’s universality. We found that maximal extension of the state space wherein sncn presents a positive Schwarzian derivative occurs at a single critical value of the shape parameter: = ≃ 0.985682. Remarkably, this value corresponds to a magic universal waveform which optimally enhances directed ratchet transport by symmetry breaking and is associated with an enhancement of chaos for ≲ 1 in parameter space with respect to the shift-symmetric map sn It should be emphasized that this change in the sign of the Schwarzian derivative is a genuine feature of the map sncn which is completely absent in the standard MSS map 000164176 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E36-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-108508GB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/PID2023-147734NB-I00 000164176 540__ $$9info:eu-repo/semantics/embargoedAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000164176 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000164176 700__ $$0(orcid)0000-0002-1625-2785$$aMartínez, Pedro J.$$uUniversidad de Zaragoza 000164176 7102_ $$12002$$2385$$aUniversidad de Zaragoza$$bDpto. Física Aplicada$$cÁrea Física Aplicada 000164176 773__ $$g484 (2025), 135036 [8 p.]$$pPhysica, D$$tPHYSICA D-NONLINEAR PHENOMENA$$x0167-2789 000164176 8564_ $$s1558932$$uhttps://zaguan.unizar.es/record/164176/files/texto_completo.pdf$$yPreprint$$zinfo:eu-repo/date/embargoEnd/2027-11-13 000164176 8564_ $$s1976548$$uhttps://zaguan.unizar.es/record/164176/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint$$zinfo:eu-repo/date/embargoEnd/2027-11-13 000164176 909CO $$ooai:zaguan.unizar.es:164176$$particulos$$pdriver 000164176 951__ $$a2025-11-27-15:16:30 000164176 980__ $$aARTICLE