4.7 Article

Librational KAM tori in the secular dynamics of the ν Andromedae planetary system

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Interdisciplinary Applications

Normal form for lower dimensional elliptic tori in Hamiltonian systems

Chiara Caracciolo

Summary: We provide a proof of convergence for an algorithm used to construct lower dimensional elliptic tori in near-integrable Hamiltonian systems. The existence of such invariant tori is demonstrated by transforming the Hamiltonian into a suitable normal form. We adapt a previously described procedure, originally used in the context of the planetary problem, and extend the proof of convergence to cases where the two sets of frequencies have similar magnitudes.

MATHEMATICS IN ENGINEERING (2022)

Article Mathematics, Applied

Elliptic tori in FPU non-linear chains with a small number of nodes

Chiara Caracciolo et al.

Summary: This study revisits an algorithm for constructing elliptic tori originally designed for planetary hamiltonian systems, and successfully applies it to FPU chains. By performing canonical transformations and using the Lie series approach, elliptic tori are constructed and stability regions are explored, showing promising results compared to numerical methods.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

Article Mathematics, Applied

COMPUTER-ASSISTED ESTIMATES FOR BIRKHOFF NORMAL FORMS

Chiara Caracciolo et al.

JOURNAL OF COMPUTATIONAL DYNAMICS (2020)

Article Astronomy & Astrophysics

The 3D secular dynamics of radial-velocity-detected planetary systems

Mara Volpi et al.

ASTRONOMY & ASTROPHYSICS (2019)

Article Computer Science, Theory & Methods

Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach

J. -Ll. Figueras et al.

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS (2017)

Article Astronomy & Astrophysics

AMD-stability and the classification of planetary systems

J. Laskar et al.

ASTRONOMY & ASTROPHYSICS (2017)

Article Astronomy & Astrophysics

THE THREE-DIMENSIONAL ARCHITECTURE OF THE υ ANDROMEDAE PLANETARY SYSTEM

Russell Deitrick et al.

ASTROPHYSICAL JOURNAL (2015)

Article Computer Science, Interdisciplinary Applications

On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system

M. Sansottera et al.

MATHEMATICS AND COMPUTERS IN SIMULATION (2013)

Article Astronomy & Astrophysics

Multi-planet extrasolar systems - detection and dynamics

Cristian Beauge et al.

RESEARCH IN ASTRONOMY AND ASTROPHYSICS (2012)

Article Astronomy & Astrophysics

Kozai resonance in extrasolar systems

A. -S. Libert et al.

ASTRONOMY & ASTROPHYSICS (2009)

Article Mathematics, Applied

On the construction of the Kolmogorov normal form for the Trojan asteroids

F Gabern et al.

NONLINEARITY (2005)

Article Astronomy & Astrophysics

Apsidal alignment in v Andromedae

EI Chiang et al.

ASTRONOMICAL JOURNAL (2001)

Article Mathematics, Applied

Improved estimates on the existence of invariant tori for Hamiltonian systems

A Celletti et al.

NONLINEARITY (2000)