@article{MTMT:2215805,
	title = {Stability of the Lagrangian point L 4 in the spatial restricted three-body problem - application to exoplanetary systems},
	url = {https://m2.mtmt.hu/api/publication/2215805},
	author = {Schwarz, R and Bazsó, A and Érdi, Bálint and Funk, B},
	doi = {10.1111/j.1365-2966.2012.21986.x},
	journal-iso = {MON NOT R ASTRON SOC},
	journal = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
	volume = {427},
	unique-id = {2215805},
	issn = {0035-8711},
	abstract = {This paper is devoted to the study of the stability of the Lagrangian point L 4 in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61° of the test particle. At moderate inclinations (~10° to ~50°), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385 - with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio-eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61°. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits. © 2012 The Authors Monthly Notices of the Royal Astronomical Society. © 2012 RAS.},
	keywords = {planetary systems; methods: numerical; celestial mechanics},
	year = {2012},
	eissn = {1365-2966},
	pages = {397-402}
}

@article{MTMT:1457203,
	title = {Dynamics of possible Trojan planets in binary systems},
	url = {https://m2.mtmt.hu/api/publication/1457203},
	author = {Schwarz, Richárd and Süli, Áron and Dvorak, R},
	doi = {10.1111/j.1365-2966.2009.15248.x},
	journal-iso = {MON NOT R ASTRON SOC},
	journal = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
	volume = {398},
	unique-id = {1457203},
	issn = {0035-8711},
	abstract = {This paper is devoted to the dynamical stability of possible Trojan planets in binaries and in binary systems where one of the substellar companions is not larger than a brown dwarf. Using numerical integrations, we investigated how the size of the stable region around the Lagrangian point L-4 depends on the mass parameter and the eccentricity of the secondary star. An additional goal of this work was to create a catalogue of all possible candidates, which could be useful for future observations to detect such objects.},
	keywords = {STABILITY; STARS; CATALOG; EXOPLANETARY SYSTEMS; TERRESTRIAL PLANETS; HABITABLE ZONES; celestial mechanics},
	year = {2009},
	eissn = {1365-2966},
	pages = {2085-2090},
	orcid-numbers = {Süli, Áron/0000-0003-0049-0233}
}

@article{MTMT:1457218,
	title = {Co-orbital terrestrial planets in exoplanetary systems: a formation scenario},
	url = {https://m2.mtmt.hu/api/publication/1457218},
	author = {Beauge, C and Sándor, Zsolt and Érdi, Bálint and Süli, Áron},
	doi = {10.1051/0004-6361:20066582},
	journal-iso = {ASTRON ASTROPHYS},
	journal = {ASTRONOMY & ASTROPHYSICS},
	volume = {463},
	unique-id = {1457218},
	issn = {0004-6361},
	abstract = {Aims. We study the formation of a hypothetical terrestrial-type body in the equilateral Lagrange points of a giant extrasolar planet. Starting from a swarm of planetesimals in stable tadpole orbits, we simulate its dynamical and collisional evolution under a wide range of different initial conditions and masses for both the Trojan population and its planetary companion. We also analyze the effects of gas drag from the interaction of the planetesimals with the nebular disk. Methods. The formation process is simulated with an N-body code that considers full gravitational interactions between the planetesimals and the giant planet. Gas interaction is modeled with Stokes and Epstein drags, where the drag coefficients are chosen following the results of full hydrodynamic simulations performed with the 2D public hydro-code FARGO. Results. In both gas-free and gas-rich scenarios, we have been able to obtain a single final terrestrial-type body in a stable tadpole orbit around one of the triangular Lagrange points of the system. However, due to gravitational instabilities within the swarm, the accretional process is not very efficient and the mass of the final planet never seems to exceed similar to 0.6 Earth masses, even when the total mass of the swarm is five times this value. Finally, we also included an orbital decay of the giant planet due to a type II migration. Although the accretional process shows evidence of a lower efficiency, a small terrestrial planet is still able to form, and follows the giant planet towards the habitable zone of the hosting star.},
	keywords = {STABILITY; MIGRATION; MOTION; ACCRETION; PLANETESIMALS; DISKS; DYNAMICAL EVOLUTION; PRIMORDIAL SOLAR NEBULA; methods : N-body simulations; planets and satellites : formation; JUPITERS TROJAN ASTEROIDS; 1/1 RESONANCE; celestial mechanics},
	year = {2007},
	eissn = {1432-0746},
	pages = {359-367},
	orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X; Süli, Áron/0000-0003-0049-0233}
}

@article{MTMT:1457216,
	title = {Secondary resonances of co-orbital motions},
	url = {https://m2.mtmt.hu/api/publication/1457216},
	author = {Érdi, Bálint and Nagy, Imre and Sándor, Zsolt and Süli, Áron and Fröhlich, Georgina},
	doi = {10.1111/j.1365-2966.2007.12228.x},
	journal-iso = {MON NOT R ASTRON SOC},
	journal = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
	volume = {381},
	unique-id = {1457216},
	issn = {0035-8711},
	abstract = {The size distribution of the stability region around the Lagrangian point L-4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that there are minimum zones in the size distribution of the stability regions, and these zones are connected with the secondary resonances between the frequencies of librational motions around L-4. The results can be applied to hypothetical Trojan planets for predicting values of the mass parameter and the eccentricity for which such objects can be expected or their existence is less probable.},
	keywords = {EVOLUTION; STABILITY; planetary systems; 3 BODIES; TRIANGULAR POINTS; EXTRASOLAR PLANETARY SYSTEMS; JUPITERS TROJAN ASTEROIDS; methods : numerical; EXOPLANETARY SYSTEMS; SOLAR-SYSTEM; ELLIPTIC RESTRICTED PROBLEM; HABITABLE ZONES; methods: numerical; celestial mechanics},
	year = {2007},
	eissn = {1365-2966},
	pages = {33-40},
	orcid-numbers = {Nagy, Imre/0000-0002-1420-4296; Sándor, Zsolt/0000-0003-1216-913X; Süli, Áron/0000-0003-0049-0233; Fröhlich, Georgina/0000-0001-6428-6536}
}

@article{MTMT:1457212,
	title = {Survey of the stability region of hypothetical habitable Trojan planets},
	url = {https://m2.mtmt.hu/api/publication/1457212},
	author = {Schwarz, Richárd and Dvorak, R and Süli, Áron and Érdi, Bálint},
	doi = {10.1051/0004-6361:20077994},
	journal-iso = {ASTRON ASTROPHYS},
	journal = {ASTRONOMY & ASTROPHYSICS},
	volume = {474},
	unique-id = {1457212},
	issn = {0004-6361},
	abstract = {Aims. In this work we study the dynamical possibility in extrasolar planetary systems that a terrestrial planet can exist in 1:1 mean motion resonance with a Jovian-like planet. We compiled a catalogue of hypothetical habitable Trojan planets, to be able to make a stability forecast for further extrasolar planetary systems discovered in the future. When speaking of habitability we also took the influence of the spectral type of the central star into account. Methods. We integrated some 106 orbits of fictitious Trojans around the Lagrangian points for up to 107 orbital periods of the primary bodies and checked the stability of the orbital elements and their chaoticity with the aid of the Lyapunov characteristic indicator and maximum eccentricity. The computations were carried out using the dynamical model of the elliptic, restricted three-body problem that consists of a central star, a gas giant moving in the habitable zone, and a hypothetical (massless) terrestrial planet. Results. Our investigations have shown that 7 exoplanetary systems can harbour habitable Trojan planets with stable orbits (HD93083, HD17051, HD28185, HD27442, HD188015, HD99109, and HD221287, which is a recently discovered system). The comparison of the investigated systems with our catalogue showed matching results, so that we can use the catalogue in practice.},
	keywords = {DYNAMICS; CAPTURE; EXPONENTS; STARS; 1/1 RESONANCE; ZONES; CO-ORBITAL MOTION; astrobiology; stars : planetary systems; ASTEROIDS; EXOPLANETARY SYSTEMS; SOLAR-SYSTEM; celestial mechanics},
	year = {2007},
	eissn = {1432-0746},
	pages = {1023-1029},
	orcid-numbers = {Süli, Áron/0000-0003-0049-0233}
}

@article{MTMT:2215810,
	title = {Stability of co-orbital motion in exoplanetary systems},
	url = {https://m2.mtmt.hu/api/publication/2215810},
	author = {Érdi, Bálint and Sándor, Zsolt},
	doi = {10.1007/s10569-004-3114-5},
	journal-iso = {CELEST MECH DYN ASTR},
	journal = {CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY},
	volume = {92},
	unique-id = {2215810},
	issn = {0923-2958},
	abstract = {The stability of co-orbital motions is investigated in such exoplanetary systems, where the only known giant planet either moves fully in the habitable zone, or leaves it for some part of its orbit. If the regions around the triangular Lagrangian points are stable, they are possible places for smaller Trojan-like planets. We have determined the nonlinear stability regions around the Lagrangian point L 4 of nine exoplanetary systems in the model of the elliptic restricted three-body problem by using the method of the relative Lyapunov indicators. According to our results, all systems could possess small Trojan-like planets. Several features of the stability regions are also discussed. Finally, the size of the stability region around L 4 in the elliptic restricted three-body problem is determined as a function of the mass parameter and eccentricity. © Springer 2005.},
	keywords = {CO-ORBITAL MOTION; EXOPLANETS; Nonlinear stability},
	year = {2005},
	eissn = {1572-9478},
	pages = {113-121},
	orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X}
}

@article{MTMT:2215817,
	title = {Symplectic mapping for Trojan-type motion in the elliptic restricted three-body problem},
	url = {https://m2.mtmt.hu/api/publication/2215817},
	author = {Sándor, Zsolt and Érdi, Bálint},
	doi = {10.1023/A:1024552601635},
	journal-iso = {CELEST MECH DYN ASTR},
	journal = {CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY},
	volume = {86},
	unique-id = {2215817},
	issn = {0923-2958},
	abstract = {A symplectic mapping for Trojan-type motion has been developed in the secularly changing elliptic restricted three-body problem. The mapping describes well the characteristics of Trojan-type dynamics at small eccentricities. By using this mapping the boundary of the stability region has been studied for different values of the initial eccentricities of hypothetical Jupiter's Trojans. It has been found that in the secularly changing elliptic case the chaotic diffusion at the border of the stability region is stronger than simply in the elliptic case. An explanation of this observation might be the destruction of the chain of islands of the 13:1 secondary resonance between the short and long period component of the Trojan-like motion, caused possibly by the indirect perturbations of Saturn.},
	keywords = {Elliptic restricted three-body problem; Trojan-type motion; Symplectic mappings; 1:1 resonance},
	year = {2003},
	eissn = {1572-9478},
	pages = {301-319},
	orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X}
}