# Dynabase (https://dynabase.org): Summary of Extreme Examples, automorphism groups (smallest degree for each group) # # Load in Sage with load(""). It defines dynabase_systems, a list of # [map, label] pairs in table order: the map as a DynamicalSystem over the field of # its table row, and its Dynabase label (dimension.sigma1.sigma2.ordinal). # Loading also (re)defines K, P, x, y. dynabase_systems = [] K = QQ P. = ProjectiveSpace(K, 1) # Morton1992, FN1997, Poonen1998, Manes2008, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020 dynabase_systems.append([DynamicalSystem([x^2, y^2], domain=P), '1.a68cf1ff.024ac6d7.1']) # GHJSX2021 dynabase_systems.append([DynamicalSystem([x^3 - y^3, -x^2*y], domain=P), '1.6a61ce14.c0adc3ec.1']) # FN1997, Ingram2012, AMT2020 dynabase_systems.append([DynamicalSystem([x^3, y^3], domain=P), '1.5fe37194.3d72adff.1']) # GHJSX2021 dynabase_systems.append([DynamicalSystem([17*x*y^3, -4*x^4 - 4*y^4], domain=P), '1.9b2c8616.14c83dd2.1']) # FN1997, dFH2018 dynabase_systems.append([DynamicalSystem([x^6 + x*y^5, y^6], domain=P), '1.ab5c2018.5ec8e92f.1']) # FN1997, dFH2018 dynabase_systems.append([DynamicalSystem([x^7 + x*y^6, y^7], domain=P), '1.e614ceae.cc96fc25.1']) # Lukas2014, CV2017, dFH2018, BS2026 dynabase_systems.append([DynamicalSystem([y^2, x^2], domain=P), '1.a35a25cc.024ac6d7.1']) # FN1997, dFH2018 dynabase_systems.append([DynamicalSystem([x^8 + x*y^7, y^8], domain=P), '1.27e72460.98bcfef1.1']) # FN1997, dFH2018 dynabase_systems.append([DynamicalSystem([x^9 + x*y^8, y^9], domain=P), '1.7b05c466.f7c38225.1']) # dFH2018, GHJSX2021 dynabase_systems.append([DynamicalSystem([y^3, x^3], domain=P), '1.ee2edc14.3d72adff.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^10 + x*y^9, y^10], domain=P), '1.7d90dee5.a689e840.1']) # dFH2018, GHJSX2021 dynabase_systems.append([DynamicalSystem([y^4, x^4], domain=P), '1.71005f25.76c4de71.1']) # GHJSX2021 dynabase_systems.append([DynamicalSystem([x^3 - 3*y^3, -3*x^2*y], domain=P), '1.ee2edc14.06479f56.1']) # dFH2018 dynabase_systems.append([DynamicalSystem([y^5, x^5], domain=P), '1.56d48bcf.d8e415c3.1']) # dFH2018 dynabase_systems.append([DynamicalSystem([y^6, x^6], domain=P), '1.61329c7f.aa38682f.1']) # dFH2018 dynabase_systems.append([DynamicalSystem([y^7, x^7], domain=P), '1.2b775e9a.84c0eaef.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^10, y^10], domain=P), '1.f0bbe529.7d4a3a0d.1']) # Miasnikov2017, dFH2018 dynabase_systems.append([DynamicalSystem([x^5 - 5*x*y^4, -5*x^4*y + y^5], domain=P), '1.56d48bcf.b239edf6.1']) # dFH2018 dynabase_systems.append([DynamicalSystem([x^11 + 66*x^6*y^5 - 11*x*y^10, -11*x^10*y - 66*x^5*y^6 + y^11], domain=P), '1.936da2cf.8bf2f4e6.1']) print("Dynabase: 19 dynamical systems in dynabase_systems")