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Bifurcations of self-similar solutions of the Fokker-Plank equations
Reduction and chaotic behavior of point vortices on a plane and a sphere
1. | Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation, Russian Federation, Russian Federation |
[1] |
Joris Vankerschaver, Eva Kanso, Jerrold E. Marsden. The geometry and dynamics of interacting rigid bodies and point vortices. Journal of Geometric Mechanics, 2009, 1 (2) : 223-266. doi: 10.3934/jgm.2009.1.223 |
[2] |
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov. Dynamics of a circular cylinder interacting with point vortices. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 35-50. doi: 10.3934/dcdsb.2005.5.35 |
[3] |
James Montaldi, Amna Shaddad. Generalized point vortex dynamics on $ \mathbb{CP} ^2 $. Journal of Geometric Mechanics, 2019, 11 (4) : 601-619. doi: 10.3934/jgm.2019030 |
[4] |
Xavier Perrot, Xavier Carton. Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 971-995. doi: 10.3934/dcdsb.2009.11.971 |
[5] |
Luis Vega. The dynamics of vortex filaments with corners. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1581-1601. doi: 10.3934/cpaa.2015.14.1581 |
[6] |
Marco Castrillón López, Pablo M. Chacón, Pedro L. García. Lagrange-Poincaré reduction in affine principal bundles. Journal of Geometric Mechanics, 2013, 5 (4) : 399-414. doi: 10.3934/jgm.2013.5.399 |
[7] |
Frederic Laurent-Polz, James Montaldi, Mark Roberts. Point vortices on the sphere: Stability of symmetric relative equilibria. Journal of Geometric Mechanics, 2011, 3 (4) : 439-486. doi: 10.3934/jgm.2011.3.439 |
[8] |
Takashi Suzuki. Brownian point vortices and dd-model. Discrete and Continuous Dynamical Systems - S, 2014, 7 (1) : 161-176. doi: 10.3934/dcdss.2014.7.161 |
[9] |
Jeffrey K. Lawson, Tanya Schmah, Cristina Stoica. Euler-Poincaré reduction for systems with configuration space isotropy. Journal of Geometric Mechanics, 2011, 3 (2) : 261-275. doi: 10.3934/jgm.2011.3.261 |
[10] |
Kristoffer Varholm. Solitary gravity-capillary water waves with point vortices. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3927-3959. doi: 10.3934/dcds.2016.36.3927 |
[11] |
Colm Connaughton, John R. Ockendon. Interactions of point vortices in the Zabusky-McWilliams model with a background flow. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1795-1807. doi: 10.3934/dcdsb.2012.17.1795 |
[12] |
Carina Geldhauser, Marco Romito. Point vortices for inviscid generalized surface quasi-geostrophic models. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2583-2606. doi: 10.3934/dcdsb.2020023 |
[13] |
Pilar Bayer, Dionís Remón. A reduction point algorithm for cocompact Fuchsian groups and applications. Advances in Mathematics of Communications, 2014, 8 (2) : 223-239. doi: 10.3934/amc.2014.8.223 |
[14] |
Denis Blackmore, Jyoti Champanerkar, Chengwen Wang. A generalized Poincaré-Birkhoff theorem with applications to coaxial vortex ring motion. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 15-33. doi: 10.3934/dcdsb.2005.5.15 |
[15] |
Gianluca Crippa, Milton C. Lopes Filho, Evelyne Miot, Helena J. Nussenzveig Lopes. Flows of vector fields with point singularities and the vortex-wave system. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2405-2417. doi: 10.3934/dcds.2016.36.2405 |
[16] |
Vikas S. Krishnamurthy. Liouville links and chains on the plane and associated stationary point vortex equilibria. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022076 |
[17] |
Chjan C. Lim, Ka Kit Tung. Introduction: Recent advances in vortex dynamics and turbulence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : i-i. doi: 10.3934/dcdsb.2005.5.1i |
[18] |
Ko-Shin Chen, Peter Sternberg. Dynamics of Ginzburg-Landau and Gross-Pitaevskii vortices on manifolds. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1905-1931. doi: 10.3934/dcds.2014.34.1905 |
[19] |
Steven M. Pederson. Non-turning Poincaré map and homoclinic tangencies in interval maps with non-constant topological entropy. Conference Publications, 2001, 2001 (Special) : 295-302. doi: 10.3934/proc.2001.2001.295 |
[20] |
Anatoli F. Ivanov. On global dynamics in a multi-dimensional discrete map. Conference Publications, 2015, 2015 (special) : 652-659. doi: 10.3934/proc.2015.0652 |
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