Periodic orbits in the Rössler system

DOI10.1016/j.cnsns.2021.105891zbMath1472.34060arXiv2101.10406OpenAlexW3124350681MaRDI QIDQ2038149

Anna Gierzkiewicz, Piotr Zgliczyński

Publication date: 9 July 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.10406

zbMATH Keywords

periodic orbitcovering relationinterval Newton methodRössler system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (2)

Nonintegrability of dynamical systems near degenerate equilibria ⋮ From the Sharkovskii theorem to periodic orbits for the Rössler system

Uses Software

• CAPD
• GitHub

Cites Work

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• Local and global behavior near homoclinic orbits
• A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
• Topological-numerical approach to the existence of periodic trajectories in ODE's
• Sharkovskiĭ theorem for multidimensional perturbations of one-dimensional maps. II
• Periodic solutions to the Rössler system
• A computer-assisted proof of symbolic dynamics in Hyperion's rotation
• An equation for continuous chaos
• Periodic solutions and invariant torus in the Rössler system
• COUNTING LOW-PERIOD CYCLES FOR FLOWS
• Computer assisted proof of chaos in the Rössler equations and in the Hénon map
• Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps
• MULTIDIMENSIONAL PERTURBATIONS OF ONE-DIMENSIONAL MAPS AND STABILITY OF SARKOVSKĬ ORDERING

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