TY - GEN

T1 - How to lose at Monte Carlo

T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020

AU - Rojas, Cristobal

AU - Yampolsky, Michael

N1 - Funding Information:
The authors would like to thank the anonymous referees for their valuable comments and helpful suggestions. C.R. was partially supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 731143, by project FONDECYT Regular No. 1190493 and project Basal PFB-03 CMM-Universidad de Chile. M.Y. was partially supported by NSERC Discovery grant.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - We consider the simplest non-linear discrete dynamical systems, given by the logistic maps fa(x)=ax(1-x) of the interval [0,1]. We show that there exist real parameters ag (0,4) for which almost every orbit of fa has the same statistical distribution in [0,1], but this limiting distribution is not Turing computable. In particular, the Monte Carlo method cannot be applied to study these dynamical systems.

AB - We consider the simplest non-linear discrete dynamical systems, given by the logistic maps fa(x)=ax(1-x) of the interval [0,1]. We show that there exist real parameters ag (0,4) for which almost every orbit of fa has the same statistical distribution in [0,1], but this limiting distribution is not Turing computable. In particular, the Monte Carlo method cannot be applied to study these dynamical systems.

KW - Logistic family

KW - Monte Carlo simulation

KW - Non-computability

KW - Physical measures

UR - http://www.scopus.com/inward/record.url?scp=85086766980&partnerID=8YFLogxK

U2 - 10.1145/3357713.3384237

DO - 10.1145/3357713.3384237

M3 - Conference contribution

AN - SCOPUS:85086766980

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1066

EP - 1072

BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Makarychev, Konstantin

A2 - Makarychev, Yury

A2 - Tulsiani, Madhur

A2 - Kamath, Gautam

A2 - Chuzhoy, Julia

PB - Association for Computing Machinery

Y2 - 22 June 2020 through 26 June 2020

ER -