Lab of Geometry and Dynamical Systems

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Publications

We gather a list (incomplete) of publications of the group. Open access version of these publications is available at https://futur.upc.edu/

2020

Books

Differentiable Manifolds, Pau Mir, Eva Miranda and Cédric Oms, 2020. file.

Technical reports (revision pending)

Baptiste Coquinot, Pau Mir and Eva Miranda,  The b-geometry of magnetic fields

Pau Mir and Eva Miranda, Geometric Quantization via cotangent models

Pau Mir and Eva Miranda, Cotangent models for non-degenerate singularities, 2020, file.

Pau Mir and Eva Miranda, Rigidity of b-cotangent lifts, 2020, file.

Published articles


MR4174297 Miranda, Eva; Presas, Francisco; Solha, Romero; Geometric quantization of almost toric manifolds. J. Symplectic Geom. 18 (2020), no. 4, 1147–1168. 

MR4137705  Mir, Pau; Miranda, Eva Rigidity of cotangent lifts and integrable systems. J. Geom. Phys. 157 (2020), 103847, 11 pp.

Accepted articles


On geometric quantization of bm-symplectic manifolds

Victor Guillemin, Eva Miranda, Jonathan Weitsman
Comments: 7 pages
Subjects: Symplectic Geometry (math.SG)

Math Z. To appear

https://www.springer.com/journal/209

 

Geometry of b^m-manifolds

Eva Miranda and Geoffrey Scott

Revista Matematica Iberoamericana, to appear

https://www.ems-ph.org/journals/journal.php?jrn=rmi

Preprints (submitted for publication)

 

[1] arXiv:2007.10314 [pdf, other]
Integrable systems on singular symplectic manifolds: From local to global
Robert Cardona, Eva Miranda
Comments: minor changes, 30 pages, 4 figures
Subjects: Symplectic Geometry (math.SG); Mathematical Physics (math-ph); Differential Geometry (math.DG); Dynamical Systems (math.DS)
[2] arXiv:2010.04770 [pdf, ps, other]
b-Structures on Lie groups and Poisson reduction
Roisin Braddell, Anna Kiesenhofer, Eva Miranda
Comments: short note, 7 pages, former appendix of v1 of arXiv:1811.11894 (v2 of arXiv:1811.11894 has been now completely rewritten and focuses on a b-symplectic slice theorem)
Subjects: Differential Geometry (math.DG); Symplectic Geometry (math.SG)
[3] arXiv:1811.11894 [pdf, other]
A b-symplectic slice theorem
Roisin Braddell, Anna Kiesenhofer, Eva Miranda
Comments: This article has been completely rewritten, 17 pages, 2 figure
Subjects: Symplectic Geometry (math.SG); Mathematical Physics (math-ph)
[4] arXiv:2010.00564 [pdf, ps, other]
On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields
Eva Miranda, Cédric Oms, Daniel Peralta-Salas
Comments: 18 pages, 2 figures, minor changes
Subjects: Symplectic Geometry (math.SG); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
[5] arXiv:2006.12477 [pdf, ps, other]
Rigidity of cotangent lifts and integrable systems
Pau Mir, Eva Miranda
Comments: 17 pages, 1 figure
Subjects: Symplectic Geometry (math.SG); Dynamical Systems (math.DS)
[6] arXiv:2005.09568 [pdf, ps, other]
The singular Weinstein conjecture
Eva Miranda, Cédric Oms
Comments: minor changes
Subjects: Symplectic Geometry (math.SG); Differential Geometry (math.DG); Dynamical Systems (math.DS)
[7] arXiv:1806.05638 [pdf, ps, other]
The geometry and topology of contact structures with singularities
Eva Miranda, Cédric Oms
Comments: 23 pages, no figures. This paper extends and improves the first parts of the previous version including also the study of folded contact forms in its analysis. The contents of the paper have changed (this is why the title is different). As for the content of singular Reeb dynamics: This has been the beginning of a new work which is now contained in a new paper: arXiv:2005.09568
Subjects: Symplectic Geometry (math.SG); Dynamical Systems (math.DS)
[8] arXiv:1911.01963 [pdf, other]
Universality of Euler flows and flexibility of Reeb embeddings
Robert Cardona, Eva Miranda, Daniel Peralta-Salas, Francisco Presas
Comments: 26pages, 3 figures, minor expository changes
Subjects: Dynamical Systems (math.DS); Analysis of PDEs (math.AP); Symplectic Geometry (math.SG)

 

2019

MR4036383 Cardona, Robert; Miranda, Eva; Peralta-Salas, Daniel Euler flows and singular geometric structures. Philos. Trans. Roy. Soc. A 377 (2019), no. 2158, 20190034, 15 pp. 76D07 (53C80 53D17)

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Review PDF Clipboard Journal Article
MR3952555 Guillemin, Victor; Miranda, Eva; Weitsman, Jonathan Desingularizing bm-symplectic structures. Int. Math. Res. Not. IMRN 2019, no. 10, 2981–2998. 53D17
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Review PDF Clipboard Journal Article 1 Citation
MR3937992 Cardona, Robert; Miranda, Eva On the volume elements of a manifold with transverse zeroes. Regul. Chaotic Dyn. 24 (2019), no. 2, 187–197. 53D05 (53D17)
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MR3904653 Braddell, Roisin; Delshams, Amadeu; Miranda, Eva; Oms, Cédric; Planas, Arnau An invitation to singular symplectic geometry. Int. J. Geom. Methods Mod. Phys. 16 (2019), suppl. 1, 1940008, 16 pp. 53D17 (37N05 53D05 53D10 70F15 70F16)
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Review PDF Clipboard Journal Article 2 Citations

 

3868426 Bolsinov, Alexey; Matveev, Vladimir S.; Miranda, Eva; Tabachnikov, Serge Open problems, questions and challenges in finite-dimensional integrable systems. Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170430, 40 pp. 37J99 (53D17)

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MR3868423  Guillemin, Victor W.; Miranda, Eva; Weitsman, Jonathan Convexity of the moment map image for torus actions on bm-symplectic manifolds. Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170420, 6 pp. 53D17
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Review PDF Clipboard Journal Article 1 Citation
MR3868420 Bouloc, D.; Miranda, E.; Zung, N. T. Singular fibres of the Gelfand-Cetlin system on u(n)∗. Philos. Trans. Roy. Soc. A 376 (2018), no. 2131, 20170423, 28 pp. 53D12 (70H06)
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Review PDF Clipboard Journal Article 1 Citation
MR3836276 Miranda, Eva; Planas, Arnau Equivariant classification of bm-symplectic surfaces. Regul. Chaotic Dyn. 23 (2018), no. 4, 355–371. 53D17 (53D05)
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Review PDF Clipboard Journal Article 1 Citation

2018

  • Amadeu Delshams, Rodrigo Schaefer, Arnold diffusion for a complete family of perturbations with two independent harmonics, Discrete Contin. Dyn. Syst. 38(12), 2018. Cite
  • Xavier Cabré, Amadeu Delshams, Marian Gidea and Chongchun Zeng, Preface of Llavefest: A Broad Perspective on Finite and Infinite Dynamical Systems, Discrete Contin. Dyn. Syst. 38(12), 2018. Cite
  • Amadeu Delshams, Vadim Kaloshin, Abraham de la Rosa, Tere M. Seara, Global Instability in the Restricted Planar Elliptic Three Body Problem, Comm. Math. Phys., 1-56, 2018, DOI 10.1007/s00220-018-3248-z. Cite
  • Amadeu Delshams, Antoni Guillamon, Gemma Huguet. Quasi-periodic perturbations of heteroclinic attractor networks, Chaos 2018(10), featured article. Cite
  • Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko, J. Tomás Lázaro, Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies, Discrete Contin. Dyn. Syst. 38(9):4483-4507, 2018. Cite
  • Amadeu Delshams, Adria Simon, Piotr Zgliczynski, Shadowing of non-transversal heteroclinic chains, J. Differential Equations 264:3619-3663, 2018. Cite
  • Alexey Bolsinov, Vladimir Matveev, Eva Miranda, Sergei Tabachnikov, Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems, arXiv:1804.03737, to appear at Philosophical Transactions of the Royal Society A, 2018. Cite
  • Victor Guillemin, Eva Miranda and Jonathan Weitsman, On geometric quantization of b-symplectic manifolds, Adv. Math. 331 (2018), 941-951. Cite
  • Damien Bouloc, Eva Miranda, Nguyen Tien Zung, Singular fibers of the Gelfand-Cetlin system on u(n) , arXiv:1803.08332, to appear at Philosophical Transactions of the Royal Society A, 2018. Cite
  • Eva Miranda and Arnau Planas, Equivariant classification of bm-symplectic surfaces, Regul. Chaotic Dyn. 23 (2018), no. 4, 355-371. Cite
  • Victor Guillemin, Eva Miranda and Jonathan Weitsman, Convexity of the moment map image for torus actions on bm-symplectic manifolds, https://arxiv.org/abs/1801.01097, to appear at Philosophical Transactions of the Royal Society A, 2018. Cite
  • Robert Cardona and Eva Miranda, Integrable systems and closed one forms, J. Geom. Phys. 131 (2018), 204-209. Cite
  • David Martinez-Torres and Eva Miranda; Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds, Regul. Chaotic Dyn. 23 (2018), no. 1, 47-53. Cite
  • Eva Miranda and Arnau Planas, Classification of bm-Nambu structures of top degree. C. R. Math. Acad. Sci. Paris 356 (2018), no. 1, 92-96. Cite
  • David Martínez-Torres, Àlvaro del Pino, Francisco Presas, Transverse geometry of foliations calibrated by non-degenerate closed 2-forms, Nagoya Mathematical Journal. 231 September 2018 , 115 - 127. Cite
  • Àlvaro del Pino, Francisco Presas, The foliated Weinstein conjecture, Int Math Res Notices (2018) Vol. 2018, 16(21), 5148–5177. Cite

2017

  • Amadeu Delshams, Marina Gonchenko, and Sergey Gonchenko. Corrigendum: On dynamics and bifurcations of area-preserving maps with homoclinic tangencies. Nonlinearity, 30(3):C2, 2017. https://doi.org/10.1088/1361-6544/aa5b4c. Cite
  • Amadeu Delshams, Anna Kiesenhofer and Eva Miranda, Examples of integrable and non integrable systems on singular symplectic manifolds, J. Geom. Phys. 115:89-97, 2017. Cite
  • Amadeu Delshams, Rodrigo Schaefer, Arnold diffusion for a complete family of perturbations, Regul. Chaotic Dyn. 22(1):78-108, 2017. Cite
  • Roisin Braddell, Amadeu Delshams, Eva Miranda, Cedric Oms and Arnau Planas, An invitation to singular symplectic geometry, to appear at the International Journal of Geometric Methods in Modern Physics, April 2017, arXiv:1705.03846. Cite
  • Victor Guillemin, Eva Miranda and Jonathan Weitsman, Desingularizing bm-symplectic structures, International Mathematics Research Notices,
    rnx126, https://doi.org/10.1093/imrn/rnx126. Cite
  • Marcel Guardia, Pau Martin, Lara Sabbagh, Tere M. Seara. Oscillatory orbits in the restricted elliptic planar three body problem. Discrete and Continuous Dynamical Systems A, 37(1): 229-256 (2017). Cite
  • Roger Casals, Jose Luis Pérez, Álvaro del Pino, Francisco Presas, Existence h-principle for Engel structures, Invent. Math. 210 (2017), no. 2, 417-451. Cite
  • Anna Kiesenhofer and Eva Miranda, Cotangent models for integrable systems, Communications in Mathematical Physics, Comm. Math. Phys. 350 (2017), no. 3, 1123-1145. Cite
  • Chiara Esposito and Eva Miranda, Rigidity of infinitesimal momentum maps, Israel J. Math. 219 (2017), no. 2, 757-781. Cite
  • David Martinez Torres, Eva Miranda, Weakly Hamiltonian actions, J. Geom. Phys. 115 (2017), 131-138. Cite
  • Victor Guillemin, Eva Miranda, Ana Pires and Geoffrey Scott, Convexity for Hamiltonian torus actions on b-symplectic manifolds, Math. Res. Lett. 24 (2017), no. 2, 363-377. Cite
  • Pedro Frejlich, David Martinez and Eva Miranda, A note on Symplectic topology on b-symplectic manifolds, J. Symplectic Geom. 15 (2017), no. 3, 719-739. Cite

2016

  • Amadeu Delshams, Marina Gonchenko, and Sergey Gonchenko. On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds. In Difference equations, discrete dynamical systems and applications, volume 180 of Springer Proc. Math. Stat., pages 107--125. Springer, Berlin, 2016. https://doi.org/10.1007/978-3-662-52927-0_8. Cite
  • Anna Kiesenhofer and Eva Miranda, Noncommutative integrable systemson b-symplectic manifolds, Regul. Chaotic Dyn. 21 (2016), no. 6, 643-659. Cite
  • Amadeu Delshams, Marian Gidea, Pablo Roldán, Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: a semi-analytical argument. Phys. D 334:29-48, 2016. Cite
  • Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez, Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio, SIAM J. Appl. Dyn. Syst. 15(2):981-1024, 2016. Cite
  • Amadeu Delshams, Rafael de la Llave, Tere M. Seara, Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion Adv. Math., 294:689-755, 2016 MR3479576. Cite
  • A. Kiesenhofer, E. Miranda and G. Scott, Action-angle variables and a KAM theorem for b-Poisson manifolds, J. Math. Pures Appl. (9) 105 2016), no. 1, 66-85. Cite