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Here, we discuss strategies to control these difficulties and succeed in obtaining an efficient sampling within a Metropolis-Hastings Monte Carlo framework. After reviewing previous successes in the case of strongly chaotic systems, we discuss the case of weakly chaotic systems. We show how different types of nonhyperbolicities limit the efficiency of previously designed sampling methods, and we discuss strategies on how to account for them. We focus on paradigmatic low-dimensional chaotic systems such as the logistic map, the Pomeau-Maneville map, and area-preserving maps with mixed phase space.<\/jats:p>","DOI":"10.1063\/1.5082640","type":"journal-article","created":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T15:40:27Z","timestamp":1555429227000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Taming chaos to sample rare events: The effect of weak chaos"],"prefix":"10.1063","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1503-9242","authenticated-orcid":false,"given":"Jorge C.","family":"Leit\u00e3o","sequence":"first","affiliation":[{"name":"Max Planck Institute for the Physics of Complex Systems 1 , 01187 Dresden, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3936-5109","authenticated-orcid":false,"given":"Jo\u00e3o M. V. 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