Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications (Q3132923)

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English	Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications	scientific article

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instance of

scholarly article

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title

Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications (English)

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31 January 2018

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full work available at URL

https://arxiv.org/abs/1706.03345

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zbMATH Keywords

periodic orbit

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(un)stable manifold

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parameterization method

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boundary value problems

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automatic differentiation

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Chebyshev polynomials

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describes a project that uses

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Leaving the moon by means of invariant manifolds of libration point orbits

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General configurations of the symmetric restricted 4-body problem

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Dynamical aspects of an equilateral restricted four-body problem

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Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem

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Branches of periodic orbits for the planar restricted 3-body problem

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Families of periodic orbits in the restricted four-body problem

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EQUILIBRIUM POINTS AND THEIR STABILITY IN THE RESTRICTED FOUR-BODY PROBLEM

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Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem

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A new family of periodic orbits for the restricted problem

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Q4457488

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Q3503406

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Geometry of weak stability boundaries

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Periodic orbits in the concentric circular restricted four-body problem and their invariant manifolds

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Q2844264

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Periodic orbits in the restricted four-body problem with two equal masses

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Hill's approximation in a restricted four-body problem

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The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces

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The parameterization method for invariant manifolds II: regularity with respect to parameters

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The parameterization method for invariant manifolds. III: Overview and applications

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Parameterization Method for Computing Quasi-periodic Reducible Normally Hyperbolic Invariant Tori

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Homoclinic and heteroclinic transfer trajectories between planar Lyapunov orbits in the Sun-Earth and Earth-Moon systems

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Computer Assisted Existence Proofs of Lyapunov Orbits at $L_2$ and Transversal Intersections of Invariant Manifolds in the Jupiter--Sun PCR3BP

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Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form

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Parameterization of invariant manifolds for periodic orbits. II: A posteriori analysis and computer assisted error bounds

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A note on the existence of a Smale horseshoe in the planar circular restricted three-body problem

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Study on Chaotic Behavior of the Restricted Four-Body Problem with an Equilateral Triangle Configuration

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Computing the scattering map in the spatial Hill's problem

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Numerical computation of heteroclinic orbits

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CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (I): POINT-TO-CYCLE CONNECTIONS

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CONTINUATION OF CONNECTING ORBITS IN 3D-ODEs (II) : CYCLE-TO-CYCLE CONNECTIONS

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The chebop system for automatic solution of differential equations

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Computing One-Dimensional Global Manifolds of Poincaré Maps by Continuation

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Reliable Computation of Robust Response Tori on the Verge of Breakdown

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Triple collisions of invariant bundles

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A numerical study of the orbits of second species of the planar circular RTBP

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Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study

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Rigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev series

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Chaotic transfers in three- and four-body systems

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GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

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Dynamics and Mission Design Near Libration Points

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Connecting orbits and invariant manifolds in the spatial restricted three-body problem

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A Computational and Geometric Approach to Phase Resetting Curves and Surfaces

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A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms

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A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results

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A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity

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The parameterization method for invariant manifolds. From rigorous results to effective computations

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Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence

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Numerical computation of normal forms around some periodic orbits of the restricted three-body problem

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A Methodology for the Numerical Computation of Normal Forms, Centre Manifolds and First Integrals of Hamiltonian Systems

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Dynamics in the center manifold of the collinear points of the restricted three-body problem

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A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods

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Q4344097

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Q4524692

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Low energy transfer to the Moon

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A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS

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On the central configurations of the planar restricted four-body problem

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Rigorous Numerics for Nonlinear Differential Equations Using Chebyshev Series

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Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields

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Automatic differentiation for Fourier series and the radii polynomial approach

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Some homoclinic phenomena in the three-body problem

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Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near $L_ 2$ in the restricted three-body problem

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Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion

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High-order expansions of invariant manifolds of libration point orbits with applications to mission design

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A Review of Invariant Manifold Dynamics of the CRTBP and Some Applications

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Introduction to Hamiltonian dynamical systems and the $N$-body problem.

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Q4524904

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NONORIENTABLE MANIFOLDS IN THREE-DIMENSIONAL VECTOR FIELDS

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Chebfun: A New Kind of Numerical Computing

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Q3125531

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Bifurcations of central configurations in the four-body problem with some equal masses

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Stability of Trojan planets in multi-planetary systems

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The existence of a Smale horseshoe in a planar circular restricted four-body problem

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Relative equilibrium solutions in the four body problem

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Q4251253

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Computing numerically with functions instead of numbers

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Q4904857

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Stationary Coexistence of Hexagons and Rolls via Rigorous Computations

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Rigorous numerics for ODEs using Chebyshev series and domain decomposition

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Symbolic dynamics and periodic orbits of the Lorenz attractor*

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Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof

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published in

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

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Identifiers

zbMATH Open document ID

1382.34053

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DOI

10.1142/S0218127417300506

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:3132923