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| 1 | INTEGRABILITY VIA INVARIANT ALGEBRAIC CURVES FOR PLANAR POLYNOMIALDIFFERENTIAL SYSTEMS显示文摘We present an introduction to the Darboux integrability theory of planar complex and real polynomial differential systems containing some improvements to the classical theory. | Colin Christopher (School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 SAA, UNITED KINGDOM) Jaume Llibre (Dopartament de Matematiques, Universitat Autonoma de Barcelona, 08193-Bellaterra, Barcelona, SPAIN) | 2000 | Annals of Differential Equations2000，16，1： | 4 |
| 2 | NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES显示文摘We consider the class of polynomial differential equations x = -y+Pn(x,y), y = x + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. Inside this class we identify a new subclass of systems having a center at the origin. We show that this subclass contains at least two subfamilies of isochro-nous centers. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centers when we perturb them inside the class of all polynomial differential systems of the above form. In particular, we present a function whose simple zeros correspond to the limit cycles vvhich bifurcate from the periodic orbits of Hamiltonian systems. | 李承治 李伟固 Jaume Llibre 张芷芬 | 2003 | Annals of Differential Equations2003，19，3： | 2 |
| 3 | Liouvillian and Analytic Integrability of the Quadratic Vector Fields Having an Invariant Ellipse显示文摘We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0. | Jaume LLIBRE Claudia VALLS | 2014 | Acta Mathematica Sinica,English Series2014，30，3： | 2 |
| 4 | Nonexistence of limit cycles for a class of structurally stable quadratic vector fields 显示文摘 | ARTES J C LLIBRE J | 2007 | Disc Contin Dyn Sys2007，17，： | 1 |
| 5 | On the optimal sta- tion keeping control of halo orbits显示文摘 | Simol C Gomez G Llibre J | 1987 | Acta Astronauti- ca1987，15，67： | 1 |
| 6 | Phase portraits of a new class of integrale quadratic vector fields 显示文摘 | LLIBRE J JESIJS S PEREZ D R | 2000 | Dynamics of continuous Discrete and Impulsive systems2000，7，： | 1 |
| 7 | Periodic orbits of a collinear restricted three-body problem 显示文摘 | Corbera M Llibre J | 2003 | Celestial Mechanics and Dynamical Astronomy2003，86，2： | 1 |
| 8 | Periodic orbits of a collinear restricted three body problem 显示文摘 | Corbera M Llibre J | 2003 | Celestial Mech Dynam Astronom2003，86，： | 1 |
| 9 | HIV-1 replication and immune dynamics are affected by raltegravir intensification of HAART-suppressed subjects显示文摘 | Buzon MJ Massanella M Llibre JM | 2010 | Nat Med2010，16，4： | 1 |
| 10 | The major genetic determinants of HIV-1control affect HLA class I peptide presentation显示文摘 | International HIV Controllers Study Pereyra F Jia X McLaren P J Telenti A de Bakker P I Walker B D Ripke S Brumme C J Pulit S L Carrington M Kadie C M Carlson J M Heckerman D Graham R R Plenge R M Deeks S G Gianniny L Crawford G Sullivan J Gonzalez E Davies L Camargo A Moore JM Beattie N Gupta S Crenshaw A Burtt N P Guiducci C Gupta N Gao X Qi Y Yuki Y Piechocka-Trocha A Cutrell E Rosenberg R Moss K L Lemay P O'Leary J Schaefer T Verma P Toth I Block B Baker B Rothchild A Lian J Proudfoot J Alvino D M Vine S Addo M M Allen T M Altfeld M Henn M R Le Gall S Streeck H Haas D W Kuritzkes D R Robbins G K Shafer R W Gulick R M Shikuma C M Haubrich R Riddler S Sax P E Daar E S Ribaudo H J Agan B Agarwal S Ahern R L Allen B L Altidor S Altschuler E L Ambardar S Anastos K Anderson B Anderson V Andrady U Antoniskis D Bangsberg D Barbaro D Barrie W Bartczak J Barton S Basden P Basgoz N Bazner S Bellos N C Benson A M Berger J Bernard N F Bernard A M Birch C Bodner S J Bolan R K Boudreaux E T Bradley M Braun J F Brndjar J E Brown S J Brown K Brown S T Burack J Bush LM Cafaro V Campbell O Campbell J Carlson R H Carmichael J K Casey K K Cavacuiti C Celestin G Chambers S T Chez N Chirch L M Cimoch P J Cohen D Cohn LE Conway B Cooper D A Cornelson B Cox D T Cristofano M V Cuchural G Jr Czartoski J L Dahman J M Daly J S Davis B T Davis K Davod S M DeJesus E Dietz C A Dunham E Dunn M E Ellerin T B Eron J J Fangman J J Farel C E Ferlazzo H Fidler S Fleenor-Ford A Frankel R Freedberg K A French N K Fuchs JD Fuller J D Gaberman J Gallant J E Gandhi R T Garcia E Garmon D Gathe J C Jr Gaultier C R Gebre W Gilman F D Gilson I Goepfert P A Gottlieb M S Goulston C Groger R K Gurley T D Haber S Hardwicke R Hardy W D Harrigan P R Hawkins T N Heath S Hecht F M Henry W K Hladek M Hoffman R P Horton J M Hsu R K Huhn G D Hunt P Hupert M J Illeman M L Jaeger H Jellinger R M John M Johnson J A Johnson K L Johnson H Johnson K Joly J Jordan W C Kauffman C A Khanlou H Killian R K Kim A Y Kim D D Kinder C A Kirchner J T Kogelman L Kojic E M Korthuis P T Kurisu W Kwon D S LaMar M Lampiris H Lanzafame M Lederman M M Lee D M Lee J M Lee M J Lee E T Lemoine J Levy J A Llibre J M Liguori M A Little S J Liu A Y Lopez A J Loutfy M R Loy D Mohammed D Y Man A Mansour M K Marconi V C Markowitz M Marques R Martin J N Martin H L Jr Mayer K H McElrath M J McGhee T A McGovern B H McGowan K McIntyre D Mcleod GX Menezes P Mesa G Metroka CE Meyer-Olson D Miller A O Montgomery K Mounzer K C Nagami E H Nagin I Nahass R G Nelson M O Nielsen C Norene D L O'Connor D H Ojikutu B O Okulicz J Oladehin O O Oldfield E C Olender S A Ostrowski M Owen WF Jr Pae E Parsonnet J Pavlatos A M Perlmutter A M Pierce M N Pincus J M Pisani L Price L J Proia L Prokesch R C Pujet H C Ramgopal M Rathod A Rausch M Ravishankar J Rhame F S Richards C S Richman D D Rodes B Rodriguez M Rose R C 3rd Rosenberg E S Rosenthal D Ross P E Rubin D S Rumbaugh E Saenz L Salvaggio M R Sanchez WC Sanjana V M Santiago S Schmidt W Schuitemaker H Sestak P M Shalit P Shay W Shirvani V N Silebi V I Sizemore J M Jr Skolnik P R Sokol-Anderson M Sosman J M Stabile P Stapleton J T Starrett S Stein F Stellbrink H J Sterman FL Stone V E Stone D R Tambussi G Taplitz R A Tedaldi E M Telenti A Theisen W Torres R Tosiello L Tremblay C Tribble M A Trinh P D Tsao A Ueda P Vaccaro A Valadas E Vanig T J Vecino I Vega V M Veikley W Wade B H Walworth C Wanidworanun C Ward D J Warner D A Weber R D Webster D Weis S Wheeler D A White D J Wilkins E Winston A Wlodaver C G van't Wout A Wright D P Yang O O Yurdin D L Zabukovic B W Zachary K C Zeeman B Zhao M | 2010 | Science2010，330，6010： | 1 |
| 11 | A set of methods in transportation network synthesis and analysis 显示文摘 | DUBOIS D BEL G LLIBRE M | 1979 | Journal of the Operational Research Society1979，30，9： | 1 |
| 12 | On the nonexistence, existence, and uniqueness of limit cycles显示文摘 | GIACOMINI H LLIBRE J VIANO M | 1996 | Nonlinearity1996，9，： | 1 |
| 13 | YSZ Obtained by MOVCD: Applications 显示文摘 | Garcia G Figueras A Llibre J | 1998 | Thin Solid Films1998，317，： | 1 |
| 14 | Algebric and topo logical classification of the homogeneous cubic vector fields in the plane显示文摘 | CIMA A LLIBR E | 1990 | Math Anal Appl1990，47，： | 1 |
| 15 | Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities显示文摘 | GINE J LLIBRE J | 2004 | J D E2004，197，： | 1 |
| 16 | New central configurations for the planar 5-body problem 显示文摘 | Jaume Llibre Luis Fernando Mello | 2008 | Celestial Mech Dyn Astr2008，100，： | 1 |
| 17 | New central configurations for the planar 5-body prohlem显示文摘 | Llibre J Mello L F | 2008 | Celestial Mech Dyn Astr2008，100，： | 1 |
| 18 | New doubly- symmetric families of comet-like periodic orbits in the spatial restricted ( N + 1 )-body problem 显示文摘 | Jaume Llibre Luci Any Roberto | 2009 | Celest Mech Dyn Astr2009，104，： | 1 |
| 19 | Limit cycles for m-piecewise discontinuous polynomial Lienard differential equations 显示文摘 | LLIBRE J TEIXEIRA M | 2015 | Z Angew Math Phys2015，66，1： | 1 |
| 20 | Local first inte- grals of differential systems and diffeomorphisms 显示文摘 | LI Weigu LLIBRE J ZHANG Xiang | 2003 | Z Angew Math Phys2003，54，： | 1 |
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