{"paper":{"title":"Where and When Orbits of Strongly Chaotic Systems Prefer to Go","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Leonid Bunimovich, Mark Bolding","submitted_at":"2017-07-13T17:28:41Z","abstract_excerpt":"We prove that transport in the phase space of the \"most strongly chaotic\" dynamical systems has three different stages. Consider a finite Markov partition (coarse graining) $\\xi$ of the phase space of such a system. In the first short times interval there is a hierarchy with respect to the values of the first passage probabilities for the elements of $\\xi$ and therefore finite time predictions can be made about which element of the Markov partition trajectories will be most likely to hit first at a given moment. In the third long times interval, which goes to infinity, there is an opposite hie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04231","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}