000170158 001__ 170158 000170158 005__ 20260407115448.0 000170158 0247_ $$2doi$$a10.1063/5.0284636 000170158 0248_ $$2sideral$$a145915 000170158 037__ $$aART-2025-145915 000170158 041__ $$aeng 000170158 100__ $$aWilczak, Daniel 000170158 245__ $$aA mechanism for growth of topological entropy 000170158 260__ $$c2025 000170158 5060_ $$aAccess copy available to the general public$$fUnrestricted 000170158 5203_ $$aTheoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. While most existing studies focus on discrete-time systems (maps), this work examines a continuous-time scenario involving global changes in the structure of an observed attractor. As a representative example, we consider the classical Rössler system. For a specific range of parameters of the system, we prove the existence of a trapping region for a certain Poincaré map, which contains a nonempty, compact, and connected invariant set on which the topological entropy of the Poincaré map is positive. Additionally, we prove the existence of a sequence of periodic orbit bifurcations that lead to an increase in the topological entropy of this Poincaré map. Our results further reveal that the topological structure of the maximal invariant set in the trapping region evolves as the parameters of the system vary. These findings are rigorously supported by computer-assisted proofs, employing interval arithmetic techniques to compute guaranteed bounds on the Poincaré map and its derivatives. 000170158 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00$$9info:eu-repo/grantAgreement/ES/DGA/E24-23R$$9info:eu-repo/grantAgreement/ES/MCINN/PID2024-156032NB-I00 000170158 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000170158 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000170158 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano, Sergio$$uUniversidad de Zaragoza 000170158 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza 000170158 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000170158 773__ $$g35, 10 (2025)$$pChaos$$tCHAOS$$x1054-1500 000170158 8564_ $$s9898549$$uhttps://zaguan.unizar.es/record/170158/files/texto_completo.pdf$$yPostprint 000170158 8564_ $$s2831025$$uhttps://zaguan.unizar.es/record/170158/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000170158 909CO $$ooai:zaguan.unizar.es:170158$$particulos$$pdriver 000170158 951__ $$a2026-03-26-14:30:44 000170158 980__ $$aARTICLE