{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T04:52:32Z","timestamp":1688619152645},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:p> In this paper, we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections and leading to escapes and captures have positive measure. Using the infinity manifold, we study capture and escape solutions in the zero-energy case. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and three anisotropic perturbations (corresponding to three relativistic correction terms) is chaotic. <\/jats:p>","DOI":"10.1142\/s0218127410026435","type":"journal-article","created":{"date-parts":[[2010,5,7]],"date-time":"2010-05-07T08:13:47Z","timestamp":1273220027000},"page":"1233-1243","source":"Crossref","is-referenced-by-count":4,"title":["ON THE ANISOTROPIC POTENTIALS OF MANEV\u2013SCHWARZSCHILD TYPE"],"prefix":"10.1142","volume":"20","author":[{"given":"CL\u00c1UDIA","family":"VALLS","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","series-title":"Memoirs of the American Mathematical Society","volume-title":"Quantitative Analysis of the Anisotropic Kepler Problem","volume":"52","author":"Casasayas J.","year":"1984"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1063\/1.532807"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1063\/1.531539"},{"key":"rf4","volume-title":"Singularities of the N-Body Problem \u2014 An Introduction to Celestial Mechanics","author":"Diacu F. N.","year":"1992"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01403170"},{"key":"rf6","first-page":"211","author":"Devaney R. L.","journal-title":"Erg. Th. Dyn. Syst."},{"key":"rf7","volume":"46","author":"Diacu F.","journal-title":"J. Math. Phys."},{"key":"rf8","first-page":"805","volume":"41","author":"Gicoma G.","journal-title":"J. Math. Phys."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1063\/1.1665596"},{"key":"rf10","volume-title":"Celestial Mechanics","author":"Hagihara Y.","year":"1975"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023648616687"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01390175"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(01)00240-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127410026435","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:28:19Z","timestamp":1565126899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127410026435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2010,4]]}},"alternative-id":["10.1142\/S0218127410026435"],"URL":"https:\/\/doi.org\/10.1142\/s0218127410026435","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4]]}}}