Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting

DOI10.1016/S0166-8641(01)00227-9zbMath1009.37027MaRDI QIDQ1862036

Zbigniew Galias

Publication date: 10 March 2003

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsLyapunov exponentsnumerical approximationinterval methodsshooting technique

Mathematics Subject Classification ID

General methods in interval analysis (65G40) Dynamical systems involving maps of the interval (37E05) Combinatorial dynamics (types of periodic orbits) (37E15) Approximation methods and numerical treatment of dynamical systems (37M99) Numerical problems in dynamical systems (65P99)

Related Items (9)

Interval arithmetic for nonlinear problem solving ⋮ Rigorous Numerical Study of Low-Period Windows for the Quadratic Map ⋮ Rigorous enclosures of rotation numbers by interval methods ⋮ INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS ⋮ Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map ⋮ Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic ⋮ REVIEW OF CHAOS COMMUNICATION BY FEEDBACK CONTROL OF SYMBOLIC DYNAMICS ⋮ A rigorous lower bound for the stability regions of the quadratic map ⋮ Interval computing periodic orbits of maps using a piecewise approach

Uses Software

• PROFIL/BIAS

Cites Work

• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS
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