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A review of the ``Third'' integral - MaRDI portal

A review of the ``Third'' integral (Q2128535)

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Language	Label	Description	Also known as
English	A review of the ``Third'' integral	scientific article

Statements

scholarly article

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A review of the ``Third'' integral (English)

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Mathematics in Engineering

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publication date

22 April 2022

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zbMATH Keywords

integrals of motion

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resonances

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density waves

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orbits in relativity and cosmology

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classical and quantum chaos

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George Contopoulos

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.3934/mine.2020022

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PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS

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A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I

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Proof That Probability Density Approaches<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mo>|</mml:mo><mml:mi>ψ</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>in Causal Interpretation of the Quantum Theory

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Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations

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Stability of periodic orbits in the elliptic, restricted three-body problem.

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The two-centre problem in general relativity: the scattering of radiation by two extreme Reissner–Nordström black-holes

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On a post-Galilean transformation appropriate to the post-Newtonian theory of Einstein, Infeld and Hoffmann

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Theoretical periodic orbits in 3-dimensional Hamiltonians

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Periodic orbits and chaos around two black holes

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Periodic orbits and chaos around two fixed black holes. II

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Ordered and chaotic Bohmian trajectories

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Convergence regions of the Moser normal forms and the structure of chaos

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Simple three-dimensional periodic orbits in a galactic-type potential

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Newtonian and relativistic periodic orbits around two fixed black holes

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The "third" Integral in Non-Smooth Potentials.

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Painleve analysis for the mixmaster universe model

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The last remake of the mixmaster universe model

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Distribution of periodic orbits and the homoclinic tangle

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Non-convergence of formal integrals of motion

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Order in de Broglie–Bohm quantum mechanics

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Partial integrability of 3d Bohmian trajectories

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Local integrability of the mixmaster model

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Analytical determination of unstable periodic orbits in area preserving maps

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QUANTUM VORTICES AND TRAJECTORIES IN PARTICLE DIFFRACTION

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Canonical transformations depending on a small parameter

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Formal integrals and Nekhoroshev stability in a mapping model for the Trojan asteroids

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Chaos in Bohmian quantum mechanics

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The speed of Arnold diffusion

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Nonconvergence of formal integrals: II. Improved estimates for the optimal order of truncation

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Nodal points and the transition from ordered to chaotic Bohmian trajectories

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Wavepacket approach to particle diffraction by thin targets: Quantum trajectories and arrival times

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Analytical invariant manifolds near unstable points and the structure of chaos

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Unstable equilibria of Hamiltonian systems

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Formal integrals for an autonomous Hamiltonian system near an equilibrium point

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Invariant KAM tori and global stability for Hamiltonian systems

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Analytical description of the structure of chaos

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Improved accuracy of the Birkhoff-Gustavson normal form and its convergence properties

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The Bianchi IX (mixmaster) cosmological model is not integrable

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Detection of Arnold diffusion in Hamiltonian systems

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Regular and chaotic dynamics.

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Stellar Dynamics: Exact Solution of the Self-Gravitation Equation

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Mixmaster Universe

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Superexponential stability of KAM tori.

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The analytic invariants of an area-preserving mapping near a hyperbolic fixed point

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New aspects in the theory of stability of Hamiltonian systems

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Convergent series expansions for quasi-periodic motions

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Extended convergence of normal forms around unstable equilibria

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Some remarks on the abundance of stable periodic orbits inside homoclinic lobes

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Integrals of motion in 3D Bohmian trajectories

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Origin of chaos in \(3\)-D Bohmian trajectories

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Study of chaos in Hamiltonian systems via convergent normal forms

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Invariant spectra of orbits in dynamical systems

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STOCHASTIC INSTABILITY OF NON-LINEAR OSCILLATIONS

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Identifiers

zbMATH Open document ID

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10.3934/mine.2020022

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2128535

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