{"paper":{"title":"Chaotic Systems with Absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph","physics.optics"],"primary_cat":"nlin.CD","authors_text":"Eduardo G. Altmann, Jefferson S. E. Portela, Tam\\'as T\\'el","submitted_at":"2013-08-14T10:26:37Z","abstract_excerpt":"Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\\kappa$ in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions $D_q$ obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses $D_1$ in terms of $\\kappa$, the positive Lyapunov exponent, the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3081","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"}