{"paper":{"title":"Chaotic Hamiltonian systems revisited: Survival probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"nlin.CD","authors_text":"S.K. Nechaev, V.A. Avetisov","submitted_at":"2009-09-24T18:27:58Z","abstract_excerpt":"We consider the dynamical system described by the area--preserving standard mapping. It is known for this system that $P(t)$, the normalized number of recurrences staying in some given domain of the phase space at time $t$ (so-clled \"survival probability\") has the power--law asymptotics, $P(t)\\sim t^{-\\nu}$. We present new semi--phenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective \"ultrametric diffusion\" on the boundary of a tree--like space with hierarchically organized transition rates. In the frameworks of our approach we have estim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4513","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"}