-
Previous Article
Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity
- DCDS Home
- This Issue
-
Next Article
Preface
Dynamics of two interacting circular cylinders in perfect fluid
1. | Institute of Computer Science, Udmurt State University, Universitetskaya ul. 1, 426034 Izhevsk, Russian Federation, Russian Federation |
2. | Institute of Computer Science, Udmurt State University, 426034 Izhevsk |
By making the radii of the cylinders infinitesimally small, we have obtained a new mechanical system which consists of two regular point vortices but with non-zero masses. The study of this system can be reduced to the study of the motion of a particle subject to potential and gyroscopic forces. A new integrable case is found. The Hamiltonian equations of motion for this system have been generalized to the case of an arbitrary number of mass vortices with arbitrary intensities. Some first integrals have been obtained. These equations expand upon the classical Kirchhoff equations of motion for $n$ point vortices.
[1] |
V. Afraimovich, J. Schmeling, Edgardo Ugalde, Jesús Urías. Spectra of dimensions for Poincaré recurrences. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 901-914. doi: 10.3934/dcds.2000.6.901 |
[2] |
B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 835-849. doi: 10.3934/dcds.2002.8.835 |
[3] |
Juan Wang, Xiaodan Zhang, Yun Zhao. Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2315-2332. doi: 10.3934/dcds.2014.34.2315 |
[4] |
Godofredo Iommi, Bartłomiej Skorulski. Multifractal analysis for the exponential family. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 857-869. doi: 10.3934/dcds.2006.16.857 |
[5] |
V. Afraimovich, Jean-René Chazottes, Benoît Saussol. Pointwise dimensions for Poincaré recurrences associated with maps and special flows. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 263-280. doi: 10.3934/dcds.2003.9.263 |
[6] |
Julien Barral, Yan-Hui Qu. On the higher-dimensional multifractal analysis. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 1977-1995. doi: 10.3934/dcds.2012.32.1977 |
[7] |
Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627 |
[8] |
Zhihui Yuan. Multifractal analysis of random weak Gibbs measures. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5367-5405. doi: 10.3934/dcds.2017234 |
[9] |
Luis Barreira. Dimension theory of flows: A survey. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3345-3362. doi: 10.3934/dcdsb.2015.20.3345 |
[10] |
Luis Barreira, César Silva. Lyapunov exponents for continuous transformations and dimension theory. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 469-490. doi: 10.3934/dcds.2005.13.469 |
[11] |
Valentin Afraimovich, Jean-Rene Chazottes and Benoit Saussol. Local dimensions for Poincare recurrences. Electronic Research Announcements, 2000, 6: 64-74. |
[12] |
Yunping Wang, Ercai Chen, Xiaoyao Zhou. Mean dimension theory in symbolic dynamics for finitely generated amenable groups. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022050 |
[13] |
Zied Douzi, Bilel Selmi. On the mutual singularity of multifractal measures. Electronic Research Archive, 2020, 28 (1) : 423-432. doi: 10.3934/era.2020024 |
[14] |
Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks and Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295 |
[15] |
Jean-Pierre Francoise, Claude Piquet. Global recurrences of multi-time scaled systems. Conference Publications, 2011, 2011 (Special) : 430-436. doi: 10.3934/proc.2011.2011.430 |
[16] |
Balázs Bárány, Michaƚ Rams, Ruxi Shi. On the multifractal spectrum of weighted Birkhoff averages. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2461-2497. doi: 10.3934/dcds.2021199 |
[17] |
Jerrold E. Marsden, Alexey Tret'yakov. Factor analysis of nonlinear mappings: p-regularity theory. Communications on Pure and Applied Analysis, 2003, 2 (4) : 425-445. doi: 10.3934/cpaa.2003.2.425 |
[18] |
Lars Olsen. First return times: multifractal spectra and divergence points. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 635-656. doi: 10.3934/dcds.2004.10.635 |
[19] |
Imen Bhouri, Houssem Tlili. On the multifractal formalism for Bernoulli products of invertible matrices. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1129-1145. doi: 10.3934/dcds.2009.24.1129 |
[20] |
Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1565-1577. doi: 10.3934/dcdsb.2020173 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]