Integrability, non-integrability, chaos and control in classical and quantum mechanics

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             University of Zielona Góra              Institute of Physics                 Institute of Astronomy       Center for Theoretical Physics, PAS

Year: 2015

1. G. Duval, A.J. Maciejewski, Integrability of potentials of degree $k\neq \pm 2$. Second order variational equations between Kolchin solvability and Abelianity, Discrete and Continuous Dynamical Systems - Series A, 2015, in print

Links:   ArXiv.org

 

Year: 2013

1. Wojciech Szumiński, Constrained N-body problems12th CONFERENCE on Dynamical Systems - Theory and ApplicationsDecember 2-5, 2013 Łódź.

Links:    Official website Prezentation 

2. Andrzej J. Maciejewski, Maria Przybylska, Leon Simpson, Wojciech SzumińskiNon-integrability of the dumbbell and point mass problem, Celestial Mechanics and Dynamical Astronomy, November 2013, Volume 117, Issue 3, pp 315-330,

Links:    Journal,  arXiv.org.

3.  Yuri N Fedorov, Andrzej J Maciejewski,  Maria Przybylska, The generalized Euler–Poinsot rigid body equations: explicit elliptic solutions, J. Phys. A: Math. Theor. 46 415201, September 2013.

Links:    Journal ArXiv.org

4.  Wojciech Szumiński, Constrained N-body problems, Workshop on Current Problems in Physics: Zielona Góra - Lviv, 23 - 25 September 2013, Zielona Góra.

Links:    Official website Conference program,  

5. Andrzej  J. Maciejewski, Maria Przybylska, Tomasz Stachowiak, Nonexistence of the final first integral in the Zipoy-Voorhees space-time, Phys. Rev. D 88, 064003 (2013) [7 pages].

Links:    Journal,  ArXiv.org

6.  Wojciech Szumiński, Dynamics of multiple pendula without gravity. Integrable systems, 27-28 June, Białystok 

Links:    Official website,  Conference program

7.  Wojciech Szumiński, Dynamics of multiple pendula without gravity. Chaos 2013, 11-14 June, Istanbul-  Turkey. 

Links:   Official website,  Conference program,     

8.  Maria Przybylska, Wojciech Szumiński, Non-integrability of flail triple pendulum, Chaos, Solitons & Fractals, Vol. 53, August 2013, Pages 60-74.

Links:    Journal,  ArXiv.org

9.  Michał Studziński, Maria Przybylska, Darboux Points and Integrability Analysis of Hamiltonian Systems with Homogeneous Rational Potentials, Physica D, Volume 249, 15 April 2013, Pages 1–15.

Links:    JournalarXiv.org.

10.   Boris S. Bardin, Andrzej J. Maciejewski, Transcendental Case in Stability Problem of Hamiltonian System with Two Degrees of Freedom in Presence of First Order Resonance, Qual. Theory Dyn. Syst. April 2013Volume 12, Issue 1pp 207-216

Links:    Journal

11.  Maria przybylska, Tomasz Stachowiak, On integrable rational potentials of the Dirac equation,  Physics Letters A, Vol. 377, Issue 12, 3 May 2013, Pages 833-841.

Links:    Journal,  arXiv.org.

 

Year: 2009

1.  Yuri N. Fedorov, Andrzej Maciejewski, Maria Przybylska, The Poisson equations in the nonholonomic Suslov problem: integrability, meromorphic and hypergeometric solutions, Nonlinearity,  Vol. 22, no 9, s. 2231--2259, 2009. 

Links:    JournalarXiv.org.

2.  Andrzej Maciejewski, Maria Przybylska, Differential Galois theory and integrability, International Journal of Geometric Methods in Modern Physics, , Vol. 6, no 8, s. 1357--1390, 2009.

Links:    JournalarXiv.org.

3.  Maria Przybylska, Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom,
Regular and Chaotic Dynamics, Vol. 14, no 2, s. 263--311, 2009.

Links:    Journal,  arXiv.org. 

4.  Maria Przybylska, Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nondegeneric case,
Regular and Chaotic Dynamics,  Vol. 14, no 3, s. 349--388, 2009.

Links:    Journal,  arXiv.org.

5.  Yuri N. Fedorov,  Andrzej Maciejewski, Maria Przybylska, The Poisson equations in the nonholonomic Suslov problem: integrability, meromorphic and hypergeometric solutions,
W: Geometric methods in physics : proceedings of the XXVIII workshop / ed. P. Kielanowski, S. Twareque Ali, A. Odzijewicz, M. Schlichenmaier, T. Voronov .- New York : American Institute of Physics, (AIP Conference Proceedings ; 1191) - s. 85--90 .- ISBN: 978-0-7354-0728-2, 2009.

Links:    Article, proceedings

6.  Simpson and G. Mullineux, Gravisma (Graphics, Visualization and Mathematics) 2009 conference, Exponentials and Motions in Geometric Algebra, 73:32, Gravisma 2009.

Links:    pdf file.

 7.  Guillaume Duval, Andrzej Maciejewski, Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials (Obstruction de Jordan a l?intégrabilité de systemes hamiltoniens avec potentiel homogene), Annales de l'Institut Fourier, Vol. 59, no 7, s. 2839--2890, 2009,

Links:    Journal,  arXiv.org.

 

Year: 2007

1.  Maria Przybylska, Finiteness of integrable n-dimensional homogeneous polynimial potentials, Physics Letters A, Vol. 369, no 3, s. 180--187, 2007.

Links:    Journal,  arXiv.org.

2.  Krzysztof Goździewski, Andrzej Maciejewski, C. Migaszewski, On the extrasolar multiplanet system around HD 16069, Astrophysical Journal, Vol. 657, s. 546--558, 2007.

Links:    Journal,  arXiv.org.

3.  Tomasz Stachowiak, Marek Szydlowski, Exact solutions in bouncing cosmology, Phys.Lett.B646:209-214, 2007.

Links:    Journal,  arXiv.org.

Year: 2014

1. A.J. Maciejewski, M. Przybylska, T. Stachowiak, Analytical method of spectra calculations in the Bargmann representation, Phys. Lett. A, Volume 378, Issue 46, 24 October 2014, Pages 3445–3451

Links:    Journal

2. W. Szumiński, M. Przybylska, Constrained $n$-body problems, in Applied Non-Linear Dynamical Systems, ed. J. Awrejcewicz, Springer Proceedings in Mathematics & Statistics vol. 93, 2014, pp 305-317

Links:   Chapter,   Book

3. G. Duval, A.J. Maciejewski, Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm2$. An application of higher order variational equations, Discrete and Continuous Dynamical Systems - Series A, 2014, Vol. 34, Iss. 11, 4589--4615

Links:   Journal,  ArXiv.org

4. Luis C. García-Naranjo, Andrzej J. Maciejewski, Juan C. Marrero, Maria Przybylska, The inhomogeneous Suslov problem, Phys. Lett. A, Volume 378, Issues 32–33, 27 June 2014, Pages 2389–2394

Links:   Journal,  ArXiv.org

5. Andrzej J. Maciejewski,  Maria Przybylska, Tomasz Stachowiak, Full spectrum of the Rabi model, Phys. A  Volume 378, Issues 1–2, 3 Jan. 2014, p.16–20.

 Links:    Journal,  ArXiv.org

 

Year: 2012

1.  Andrzej Maciejewski, Maria Przybylska, Tomasz Stachowiak, How to calculate spectra of Rabi and related modelspreprint.

Links:   ArXiv.org

2.  Andrzej Maciejewski, Maria Przybylska Haruo Yoshida, Necessary conditions for the existence of additional first integrals for Hamiltonian systems with homogeneous potential, Nonlinearity,  Vol. 25, no 2, s. 255--277, 2012.

Links:    Journal,   ArXiv.org.

3.  Andrzej Maciejewski, Maria Przybylska, Integrable variational equations of non-integrable systems, Regular and Chaotic Dynamics, Vol.17, no 3-4, s. 337--358,2012.

Links:    Journal,  ArXiv.org.

4.  Wojciech Szumiński, Mini-conference Integrable Systems,  21-22 June 2012, Olsztyn,  Dynamics of multiple pendula.

Links:    Oficial website,    

5.  Wojciech Szumiński,  Dynamics of multiple pendula, the bachelor thesis, July 2012.  .

Links:   

6.  Tomasz Stachowiak, Maria Przybylska, On integrable rational potentials of the Dirac equation,  Phys. Lett. A, Volume 377, Issue 12, 3 May 2013, Pages 833-841.

Links:    Journal,  arXiv.org.

7.  Krzysztof Gozdziewski, Ilham Nasiroglu, Aga Slowikowska, Klaus Beuermann, Gottfried Kanbach, Bartosz Gauza, Andrzej J. Maciejewski, Robert Schwarz, Axel D. Schwope, Tobias C. Hinse, Nader Haghighipour, Vadim Burwitz, Mariusz Slonina, Arne Rau, On the HU Aquarii planetary system hypothesis,
Monthly Notices of the Royal Astronomical Society, Vol. 425, Issue 2, s. 930–-949, 11 September 2012.

Links:    Journal,  arXiv.org.

 

Year: 2010

1.   Andrzej Maciejewski, Maria Przybylska, Partial integrability of Hamiltonian systems with homogenous potential, Regular and Chaotic Dynamics, Vol. 15, no 4-5, s. 551--563, 2010.

Links:    Journal,  arXiv.org.

2.   Andrzej Maciejewski, Maria Przybylska, Haruo Yoshida,  Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces, Journal of Physics A : Mathematical and Theoretical,  Vol. 43, no 38, s. [15], 2010.

Links:    Journal,  arXiv.org.

3.   Guy Casale, Guillaume Duval, Andrzej Maciejewski, Maria Przybylska, Integrability of Hamiltonian systems with homogeneous potentials of degree zero, Physics Letters A, Vol. 374, no 3, s. 448--452, 2010.

Links:    Journal,  arXiv.org.  

4. Jakub Mielczarek, Tomasz Stachowiak, Marek Szydlowski, Vortex in axion condensate as a dark matter halo,  Int.J.Mod.Phys.D19:1843-1855, 2010.

Links:    JournalarXiv.org.

5.  Mikhail Vereshchagin, Andrzej J. Maciejewski, Krzysztof Gozdziewski, Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body,
Monthly Notices of the Royal Astronomical Society, Vol. 403, Issue 2, pages 848–858, 2010.

Links:    Journal,  arXiv.org.

 

Year: 2006

1.  Tomasz Stachowiak, Marek Szydłowski, Andrzej Maciejewski, Nonitegrability of density perturbations in the Friedmann-Robertson-Walker universe,
Journal of Mathematical Physics, Vol. 47, s. 032502-1--032502-11, 2006.

Links:    Journal,  arXiv.org.

2.  Krzysztof Goździewski, Maciej Konacki, Andrzej Maciejewski, Orbital configurations and dynamical stability of multiplanet systems around sun-like stars HD 202206, 14 Herculis, HD 37124, and HD 108874,  Astrophysical Journal, Vol. 645, s. 688--703, 2006.

Links:    Journal,  arXiv.org.

3.  B. A. Steves, Andrzej Maciejewski, M. Hendry, Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical System, Springer - 342 s. - (NATO Science Series II : Mathematics, Physics and Chemistry ; Vol. 227) .- ISBN: 978-1-4020-4708-3, 2006.

Links:   Book

4.  Marek Szydlowski, Tomasz Stachowiak, Radoslaw Wojtak, Towards testing interacting cosmology by distant type Ia supernovae, Phys.Rev.D73:063516, 2006.

Links:    Journal,  arXiv.org.

5.  Mariusz P. Dabrowski, Tomasz Stachowiak, Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion, Annals Phys. 321,  771-812, 2006.

Links:    Journal,  arXiv.org.