Generalized periodic orbits of the time-periodically forced Kepler problem accumulating at the center and of circular and elliptic restricted three-body problems
Sign Up to like & getrecommendations! Published in 2021 at "Mathematische Annalen"
DOI: 10.1007/s00208-021-02339-8
Abstract: In this paper, we consider a time-periodically forced Kepler problem in any dimension, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there… read more here.
Keywords: periodically forced; center; time periodically; forced kepler ... See more keywords
Nonexistence of Periodic Orbits for Forced–Damped Potential Systems in Bounded Domains
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-020-09607-y
Abstract: We prove $$L^r$$ L r -estimates on periodic solutions of periodically forced, linearly damped mechanical systems with polynomially bounded potentials. The estimates are applied to obtain a nonexistence result of periodic solutions in bounded domains,… read more here.
Keywords: damped potential; bounded domains; forced damped; orbits forced ... See more keywords
Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies
Sign Up to like & getrecommendations! Published in 2017 at "Astrophysics and Space Science"
DOI: 10.1007/s10509-017-3148-2
Abstract: Research on the stabilities of periodic orbits is useful for selection of parking orbits in asteroid and comet missions. In this paper, retrograde near-circular periodic orbits near equatorial planes (RNPOEP) of small irregular bodies are… read more here.
Keywords: circular periodic; orbits near; near equatorial; near circular ... See more keywords
Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem
Sign Up to like & getrecommendations! Published in 2018 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-018-9834-8
Abstract: We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study… read more here.
Keywords: circular elliptic; restricted three; periodic orbits; elliptic restricted ... See more keywords
A database of planar axisymmetric periodic orbits for the Solar system
Sign Up to like & getrecommendations! Published in 2018 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-018-9844-6
Abstract: A multiple grid search strategy is implemented to generate a broad database of axisymmetric three-body periodic orbits for planets and main planetary satellites in the Solar system. The periodic orbit search is performed over 24… read more here.
Keywords: grid search; search; solar system; database ... See more keywords
Uniform Generators, Symbolic Extensions with an Embedding, and Structure of Periodic Orbits
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-018-9674-y
Abstract: For a topological dynamical system $$(X,T)$$(X,T) we define a uniform generator as a finite measurable partition such that the symmetric cylinder sets in the generated process shrink in diameter uniformly to zero. The problem of… read more here.
Keywords: extensions embedding; zero dimensional; uniform generators; symbolic extensions ... See more keywords
Reeb’s Theorem and Periodic Orbits for a Rotating Hénon–Heiles Potential
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-019-09814-6
Abstract: We apply Reeb’s theorem to prove the existence of periodic orbits in the rotating Hénon–Heiles system. To this end, a sort of detuned normal form is calculated that yields a reduced system with at most… read more here.
Keywords: non heiles; rotating non; orbits rotating; periodic orbits ... See more keywords
Periodic orbits of a conservative 2-DOF vibro-impact system by piecewise continuation: bifurcations and fractals
Sign Up to like & getrecommendations! Published in 2019 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-04734-4
Abstract: The exact periodic orbits of a conservative 2-degree-of-freedom vibro-impact system with stereo-mechanical impact model is studied using a piecewise continuation method. Feasible initial guesses are extracted from grazing solution points so that each branch of… read more here.
Keywords: orbits conservative; system; impact; periodic orbits ... See more keywords
The high forecasting complexity of stochastically perturbed periodic orbits limits the ability to distinguish them from chaos
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DOI: 10.1007/s11071-020-05920-z
Abstract: A long-standing question in applications of dynamical systems theory is how to distinguish noisy signals from chaotic steady states. Information-theoretic measures hold promise to resolve this problem. We apply two such measures to numerically computed… read more here.
Keywords: stochastically perturbed; perturbed periodic; chaos; periodic orbits ... See more keywords
Periodic Orbits and Bifurcations of the Vibrational Modes of the Ozone Molecule at High Energies
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DOI: 10.1007/s11182-020-01923-w
Abstract: The study of quantum states near the dissociation threshold is necessary both to understand the formation of molecules and to explore accurately chemical reactions. Quantum calculations of highly excited states can be complemented by methods… read more here.
Keywords: orbits bifurcations; high energies; ozone molecule; bifurcations vibrational ... See more keywords
Stabilizing periodic orbits of a class of mechanical systems with impulse effects: A Lyapunov constraint approach
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Control, Automation and Systems"
DOI: 10.1007/s12555-016-0387-x
Abstract: This paper study the stabilization of mechanical system with impulse effects around a hybrid limit cycle, the proposed control approach is based on LaSalle’s invariance principle for hybrid systems and Layounov constraint based method. Theorem… read more here.
Keywords: impulse effects; periodic orbits; constraint; orbits class ... See more keywords