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Journal of Dynamical and Control Systems, ISSN 1079-2724, 7/2018, Volume 24, Issue 3, pp. 425 - 438
We prove that the Zarisky closure of the monodromy group of the polynomial x 2 y 2(1 − x − y) is the symplectic group Sp(4,ℂ) $Sp(4,\mathbb {C})$. This shows... 
34C05 | Vibration, Dynamical Systems, Control | Picard-Fuchs equation | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 37F75 | Mathematics | Dynamical Systems and Ergodic Theory | Limit cycle | Monodromy | Dynamical Systems
Journal Article
Journal of Dynamical and Control Systems, ISSN 1079-2724, 07/2018, Volume 24, Issue 3, p. 425
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s10883-017-9379-2 We prove... 
Journal Article
Inventiones Mathematicae, ISSN 0020-9910, 2001, Volume 143, Issue 3, pp. 449 - 497
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2016, Volume 144, Issue 10, pp. 4205 - 4219
We prove that the cyclicity of a slow-fast integrable system of Darboux type with a double heteroclinic loop is finite and uniformly bounded. 
Limit cycle | Slow-fast system | Double heteroclinic loop | MATHEMATICS | double heteroclinic loop | MATHEMATICS, APPLIED | limit cycle | ABELIAN-INTEGRALS | VECTOR-FIELDS | LIMIT-CYCLES | Dynamical Systems | Mathematics
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 03/2001, Volume 143, Issue 3, pp. 449 - 497
Let H(x,y) be a real cubic polynomial with four distinct critical values (in a complex domain) and let X H =H y -H x be the corresponding Hamiltonian vector... 
Mathematics, general | Mathematics | MATHEMATICS | NUMBER | PERTURBATIONS | HAMILTONIAN VECTOR-FIELDS | SINGULARITIES | ABELIAN-INTEGRALS | SYSTEMS | LIMIT-CYCLES | ZEROS | Studies
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2014, Volume 89, Issue 1, pp. 125 - 155
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 7/2013, Volume 47, Issue 3, pp. 174 - 186
We prove that the number of limit cycles which bifurcate from a two-saddle loop of an analytic planar vector field X 0 under an arbitrary finite-parameter... 
two-saddle loop | Functional Analysis | Analysis | Mathematics | finite cyclicity | limit cycles | heteroclinic loop | MATHEMATICS | MATHEMATICS, APPLIED | CYCLICITY | ABELIAN-INTEGRALS | LOOPS | ZEROS
Journal Article
Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 10/2008, Volume 28, Issue 5, pp. 1497 - 1507
Let Pi be an open period annulus of a plane analytic vector field X-0. We prove that the maximal number of limit cycles which bifurcate from Pi under a given... 
MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATIONS | LIMIT-CYCLES | QUADRATIC HAMILTONIAN-SYSTEMS
Journal Article
Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 3/2011, Volume 42, Issue 1, pp. 1 - 23
We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic... 
34C05 | limit cycle | two-saddle loop | Theoretical, Mathematical and Computational Physics | analytic vector field | Mathematics, general | Mathematics | 34C08 | 34C07 | Limit cycle | Analytic vector field | Two-saddle loop | SUCCESSIVE DERIVATIVES | UNFOLDINGS | INTEGRALS | MATHEMATICS | PERIOD ANNULI | FINITE CYCLICITY | MAP
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2016, Volume 260, Issue 5, pp. 3963 - 3990
The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field... 
MATHEMATICS | NUMBER | LIMIT-CYCLES | MAP | ABELIAN-INTEGRALS | ZEROS | Dynamical Systems | Mathematics
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 12/2019, Volume 157, p. 102796
We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we... 
Zeros of elliptic integrals | Limit cycles | Duffing oscillator | MATHEMATICS, APPLIED | NUMBER | BIFURCATIONS | ABELIAN-INTEGRALS | MAP | ZEROS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2015, Volume 424, Issue 1, pp. 774 - 784
The cyclicity of the exterior period annulus of the asymmetrically perturbed Duffing oscillator is a well known problem extensively studied in the literature.... 
16th Hilbert problem | Limit cycles | Zeros of elliptic integrals depending on parameters | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | BIFURCATIONS | ABELIAN-INTEGRALS | LIMIT-CYCLES | ZEROS | Dynamical Systems | Mathematics
Journal Article
by Khachatryan, V and Sirunyan, A M and Tumasyan, A and Adam, W and Bergauer, T and Dragicevic, M and Erö, J and Fabjan, C and Friedl, M and Frühwirth, R and Ghete, V M and Hammer, J and Hänsel, S and Hartl, C and Hoch, M and Hörmann, N and Hrubec, J and Jeitler, M and Kasieczka, G and Kiesenhofer, W and Krammer, M and Liko, D and Mikulec, I and Pernicka, M and Rohringer, H and Schöfbeck, R and Strauss, J and Taurok, A and Teischinger, F and Waltenberger, W and Walzel, G and Widl, E and Wulz, C.-E and Mossolov, V and Shumeiko, N and Suarez Gonzalez, J and Benucci, L and Ceard, L and De Wolf, E A and Janssen, X and Maes, T and Mucibello, L and Ochesanu, S and Roland, B and Rougny, R and Selvaggi, M and Van Haevermaet, H and Van Mechelen, P and Van Remortel, N and Adler, V and Beauceron, S and Blyweert, S and D’Hondt, J and Devroede, O and Kalogeropoulos, A and Maes, J and Maes, M and Tavernier, S and Van Doninck, W and Van Mulders, P and Villella, I and Chabert, E C and Charaf, O and Clerbaux, B and De Lentdecker, G and Dero, V and Gay, A P. R and Ham-mad, G H and Hreus, T and Marage, P E and Vander Velde, C and Vanlaer, P and Wickens, J and Costantini, S and Grunewald, M and Klein, B and Marinov, A and Ryckbosch, D and Thyssen, F and Tytgat, M and Vanelderen, L and Verwilligen, P and Walsh, S and Zaganidis, N and Basegmez, S and Bruno, G and Caudron, J and De Favereau De Jeneret, J and Delaere, C and Demin, P and Favart, D and Giammanco, A and Grégoire, G and Hollar, J and Lemaitre, V and Militaru, O and Ovyn, S and Pagano, D and Pin, A and Piotrzkowski, K and ... and CMS Collaboration and The CMS collaboration
Journal of High Energy Physics, ISSN 1126-6708, 9/2010, Volume 2010, Issue 9, pp. 1 - 38
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2015, Volume 32, Issue 2, pp. 307 - 324
We prove that the number of limit cycles which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic... 
UNFOLDINGS | MATHEMATICS, APPLIED | CYCLICITY | NUMBER | APPEAR | ALIEN LIMIT-CYCLES | ELLIPTIC SEGMENT LOOPS | PERIOD ANNULI | SYSTEMS | PLANAR VECTOR-FIELDS | HILBERTS 16TH PROBLEM
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 357, Issue 1, pp. 69 - 76
We study the stratum in the set of all quadratic differential systems x ˙ = P 2 ( x , y ) , y ˙ = Q 2 ( x , y ) with a center, known as the codimension-four... 
Quadratic codimension-four centers | Limit cycles | Zeros of Abelian integrals | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTONIAN-SYSTEMS
Journal Article
11/2018
This is an extended version of two lectures given during the Zagreb Dynamical Systems Workshop, October 22-26, 2018. 
Mathematics - Dynamical Systems
Journal Article
by Chatrchyan, S and Khachatryan, V and Sirunyan, A.M and Tumasyan, A and Adam, W and Bergauer, T and Dragicevic, M and Erö, J and Fabjan, C and Friedl, M and Frühwirth, R and Ghete, V.M and Hartl, C and Hörmann, N and Hrubec, J and Jeitler, M and Kiesenhofer, W and Knünz, V and Krammer, M and Krätschmer, I and Liko, D and Mikulec, I and Rabady, D and Rahbaran, B and Rohringer, H and Schöfbeck, R and Strauss, J and Taurok, A and Treberer-Treberspurg, W and Waltenberger, W and Wulz, C.-E and Mossolov, V and Shumeiko, N and Suarez Gonzalez, J and Alderweireldt, S and Bansal, M and Bansal, S and Beaumont, W and Cornelis, T and De Wolf, E.A and Janssen, X and Knutsson, A and Luyckx, S and Mucibello, L and Ochesanu, S and Roland, B and Rougny, R and Van Haevermaet, H and Van Mechelen, P and Van Remortel, N and Van Spilbeeck, A and Blekman, F and Blyweert, S and D'Hondt, J and Devroede, O and Heracleous, N and Kalogeropoulos, A and Keaveney, J and Kim, T.J and Lowette, S and Maes, M and Olbrechts, A and Python, Q and Strom, D and Tavernier, S and Van Doninck, W and Van Lancker, L and Van Mulders, P and Van Onsem, G.P and Villella, I and Caillol, C and Clerbaux, B and De Lentdecker, G and Favart, L and Gay, A.P.R and Léonard, A and Marage, P.E and Mohammadi, A and Perniè, L and Reis, T and Seva, T and Thomas, L and Vander Velde, C and Vanlaer, P and Wang, J and Adler, V and Beernaert, K and Benucci, L and Cimmino, A and Costantini, S and Crucy, S and Dildick, S and Garcia, G and Klein, B and Lellouch, J and Mccartin, J and Ocampo Rios, A.A and Ryckbosch, D and Salva Diblen, S and Sigamani, M and ... and CMS Collaboration and Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Journal of Instrumentation, ISSN 1748-0221, 2014, Volume 9, Issue 10, pp. P10009 - P10009
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2014, Volume 89, Issue 1, pp. 125 - 155
In the present paper we solve the following different but interrelated problems: (a)~the moment problem on Riemann surfaces, (b) the vanishing problem for... 
Potential theory | Integral transforms, operational calculus | POLYNOMIALS | MATHEMATICS | ZERO | SEGMENT | CYCLES | Moment problem | POWERS | Abelian integrals
Journal Article
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