{"paper":{"title":"Fractal analysis of Neimark-Sacker bifurcation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Computing), Faculty of Electrical Engineering, L. Horvat Dmitrovi\\'c (University of Zagreb","submitted_at":"2012-10-31T00:04:10Z","abstract_excerpt":"In this paper we show how a change of box dimension of the orbits of two-dimensional discrete dynamical systems is connected to bifurcations in a nonhyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems. Namely, at the bifurcation point the box dimension changes from zero to a certain positive value which is connected to the type of bifurcation. First, we study a two-dimensional discrete dynamical system with only one multiplier on the unit circle, and get the result for the box dimension of the orbit on the center manifold. Then we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8202","kind":"arxiv","version":1},"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"}