000130457 001__ 130457
000130457 005__ 20240125162930.0
000130457 0247_ $$2doi$$a10.1007/s11071-020-05930-x
000130457 0248_ $$2sideral$$a120333
000130457 037__ $$aART-2020-120333
000130457 041__ $$aeng
000130457 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, R.$$uUniversidad de Zaragoza
000130457 245__ $$aDistribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system
000130457 260__ $$c2020
000130457 5203_ $$aWe provide rigorous computer-assisted proofs of the existence of different dynamical objects, like stable families of periodic orbits, bifurcations and stable invariant tori around them, in the paradigmatic Hénon–Heiles system. There are in the literature a large number of articles with numerical simulations on this system, and other open Hamiltonians, but only a few give a rigorous guarantee of simulations. In this article, we present the necessary link between the numerical simulations and the mathematical structure of the system, since it is relevant to provide evidence of the existence of some of the different objects detected numerically to evaluate the quality of the numerical results. Remarkably, we present a proof of the existence of stable regions in the non-hyperbolic and hyperbolic regimes classically established for the Hénon–Heiles system. In particular, we prove the important results of the existence of bounded stable regular regions located within the escape region, far from the regime of the KAM islands, which are called “safe regions”.
000130457 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-096026-B-I00$$9info:eu-repo/grantAgreement/ES/UZ/CUD2019-CIE-04
000130457 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000130457 590__ $$a5.022$$b2020
000130457 591__ $$aMECHANICS$$b16 / 135 = 0.119$$c2020$$dQ1$$eT1
000130457 591__ $$aENGINEERING, MECHANICAL$$b16 / 133 = 0.12$$c2020$$dQ1$$eT1
000130457 592__ $$a1.252$$b2020
000130457 593__ $$aAerospace Engineering$$c2020$$dQ1
000130457 593__ $$aApplied Mathematics$$c2020$$dQ1
000130457 593__ $$aOcean Engineering$$c2020$$dQ1
000130457 593__ $$aElectrical and Electronic Engineering$$c2020$$dQ1
000130457 593__ $$aMechanical Engineering$$c2020$$dQ1
000130457 593__ $$aControl and Systems Engineering$$c2020$$dQ1
000130457 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000130457 700__ $$aWilczak, D.
000130457 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000130457 773__ $$g102 (2020), 403–416$$pNonlinear dyn.$$tNonlinear Dynamics$$x0924-090X
000130457 8564_ $$s5526106$$uhttps://zaguan.unizar.es/record/130457/files/texto_completo.pdf$$yPostprint
000130457 8564_ $$s1964422$$uhttps://zaguan.unizar.es/record/130457/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000130457 909CO $$ooai:zaguan.unizar.es:130457$$particulos$$pdriver
000130457 951__ $$a2024-01-25-15:12:21
000130457 980__ $$aARTICLE