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A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
Topological invariants for singularities of real vector fields in dimension three
1. | Dpto. de Estadística e Investigación Operativa, Universidad de Alicante, 03690 San Vicente del Raspeig, Alicante, Spain |
2. | Foundation Getulio Vargas, Rio de Janeiro, Brazil |
3. | Dpto. Álgebra, Geometría y Topología, Universidad de Valladolid, 47005 Valladolid, Spain |
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C. Alonso-González, M. I. Camacho, F. Cano. Topological classification of multiple saddle connections. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 395-414. doi: 10.3934/dcds.2006.15.395 |
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Robert Roussarie. A topological study of planar vector field singularities. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5217-5245. doi: 10.3934/dcds.2020226 |
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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 |
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Benjamin Dozier. Equidistribution of saddle connections on translation surfaces. Journal of Modern Dynamics, 2019, 14: 87-120. doi: 10.3934/jmd.2019004 |
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Primitivo B. Acosta-Humánez, J. Tomás Lázaro, Juan J. Morales-Ruiz, Chara Pantazi. On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1767-1800. doi: 10.3934/dcds.2015.35.1767 |
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David J. W. Simpson. On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3803-3830. doi: 10.3934/dcds.2014.34.3803 |
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Tiago de Carvalho, Bruno Freitas. Birth of an arbitrary number of T-singularities in 3D piecewise smooth vector fields. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4851-4861. doi: 10.3934/dcdsb.2019034 |
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Marko Budišić, Stefan Siegmund, Doan Thai Son, Igor Mezić. Mesochronic classification of trajectories in incompressible 3D vector fields over finite times. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 923-958. doi: 10.3934/dcdss.2016035 |
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Lev M. Lerman, Elena V. Gubina. Nonautonomous gradient-like vector fields on the circle: Classification, structural stability and autonomization. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1341-1367. doi: 10.3934/dcdss.2020076 |
[10] |
José Ginés Espín Buendía, Víctor Jiménez Lopéz. A topological characterization of the $\omega$-limit sets of analytic vector fields on open subsets of the sphere. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1143-1173. doi: 10.3934/dcdsb.2019010 |
[11] |
Alexandre A. P. Rodrigues. Moduli for heteroclinic connections involving saddle-foci and periodic solutions. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3155-3182. doi: 10.3934/dcds.2015.35.3155 |
[12] |
Leonardo Câmara, Bruno Scárdua. On the integrability of holomorphic vector fields. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 481-493. doi: 10.3934/dcds.2009.25.481 |
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Jifeng Chu, Zhaosheng Feng, Ming Li. Periodic shadowing of vector fields. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3623-3638. doi: 10.3934/dcds.2016.36.3623 |
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Anirban Banerjee, Jürgen Jost. Spectral plot properties: Towards a qualitative classification of networks. Networks and Heterogeneous Media, 2008, 3 (2) : 395-411. doi: 10.3934/nhm.2008.3.395 |
[15] |
Chang-Shou Lin, Lei Zhang. Classification of radial solutions to Liouville systems with singularities. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2617-2637. doi: 10.3934/dcds.2014.34.2617 |
[16] |
Ulrike Kant, Werner M. Seiler. Singularities in the geometric theory of differential equations. Conference Publications, 2011, 2011 (Special) : 784-793. doi: 10.3934/proc.2011.2011.784 |
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Felicia Maria G. Magpantay, Xingfu Zou. Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback connections. Mathematical Biosciences & Engineering, 2010, 7 (2) : 421-442. doi: 10.3934/mbe.2010.7.421 |
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Gareth Ainsworth, Yernat M. Assylbekov. On the range of the attenuated magnetic ray transform for connections and Higgs fields. Inverse Problems and Imaging, 2015, 9 (2) : 317-335. doi: 10.3934/ipi.2015.9.317 |
[19] |
BronisŁaw Jakubczyk, Wojciech Kryński. Vector fields with distributions and invariants of ODEs. Journal of Geometric Mechanics, 2013, 5 (1) : 85-129. doi: 10.3934/jgm.2013.5.85 |
[20] |
Davi Obata. Symmetries of vector fields: The diffeomorphism centralizer. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4943-4957. doi: 10.3934/dcds.2021063 |
2020 Impact Factor: 1.392
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