-
Previous Article
Optimal control of dynamical systems with polynomial impulses
- DCDS Home
- This Issue
-
Next Article
Necessary conditions for a weak minimum in optimal control problems with integral equations on a variable time interval
Integral representations for bracket-generating multi-flows
1. | Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63 - 35121 - Padova (PD), Italy, Italy |
References:
[1] |
A. A. Agračev and R. V. Gamkrelidze, Exponential representation of flows and a chronological enumeration, Mat. Sb. (N.S.), 107 (1978), 467-532, 639. |
[2] |
A. A. Agračev and R. V. Gamkrelidze, Chronological algebras and nonstationary vector fields, in Problems in geometry, (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 11 (1980), 135-176, 243. |
[3] |
M. Bramanti, L. Brandolini and M. Pedroni, Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality, Forum Math., 25 (2013), 703-769.
doi: 10.1515/form.2011.133. |
[4] |
A. Montanari and D. Morbidelli, Nonsmooth Hörmander vector fields and their control balls, Trans. Amer. Math. Soc., 364 (2012), 2339-2375.
doi: 10.1090/S0002-9947-2011-05395-X. |
[5] |
A. Montanari and D. Morbidelli, Almost exponential maps and integrability results for a class of horizontally regular vector fields, Potential Anal., 38 (2013), 611-633.
doi: 10.1007/s11118-012-9289-6. |
[6] |
A. Montanari and D. Morbidelli, Step-$s$ involutive families of vector fields, their orbits and the Poincaré inequality, J. Math. Pures Appl. (9), 99 (2013), 375-394.
doi: 10.1016/j.matpur.2012.09.005. |
[7] |
A. Montanari and D. Morbidelli, Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields, J. Geom. Anal., 24 (2014), 687-720.
doi: 10.1007/s12220-012-9351-z. |
[8] |
F. Rampazzo and H. J. Sussmann, Set-valued differentials and a nonsmooth version of Chow-Rashevski's theorem, in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, December 2001, IEEE Publications, (2001), 2613-2618. |
[9] |
F. Rampazzo and H. J. Sussmann, Commutators of flow maps of nonsmooth vector fields, J. Differential Equations, 232 (2007), 134-175.
doi: 10.1016/j.jde.2006.04.016. |
[10] |
E. T. Sawyer and R. L. Wheeden, Hölder continuity of weak solutions to subelliptic equations with rough coefficients, Mem. Amer. Math. Soc., 180 (2006), x+157pp.
doi: 10.1090/memo/0847. |
show all references
References:
[1] |
A. A. Agračev and R. V. Gamkrelidze, Exponential representation of flows and a chronological enumeration, Mat. Sb. (N.S.), 107 (1978), 467-532, 639. |
[2] |
A. A. Agračev and R. V. Gamkrelidze, Chronological algebras and nonstationary vector fields, in Problems in geometry, (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 11 (1980), 135-176, 243. |
[3] |
M. Bramanti, L. Brandolini and M. Pedroni, Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality, Forum Math., 25 (2013), 703-769.
doi: 10.1515/form.2011.133. |
[4] |
A. Montanari and D. Morbidelli, Nonsmooth Hörmander vector fields and their control balls, Trans. Amer. Math. Soc., 364 (2012), 2339-2375.
doi: 10.1090/S0002-9947-2011-05395-X. |
[5] |
A. Montanari and D. Morbidelli, Almost exponential maps and integrability results for a class of horizontally regular vector fields, Potential Anal., 38 (2013), 611-633.
doi: 10.1007/s11118-012-9289-6. |
[6] |
A. Montanari and D. Morbidelli, Step-$s$ involutive families of vector fields, their orbits and the Poincaré inequality, J. Math. Pures Appl. (9), 99 (2013), 375-394.
doi: 10.1016/j.matpur.2012.09.005. |
[7] |
A. Montanari and D. Morbidelli, Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields, J. Geom. Anal., 24 (2014), 687-720.
doi: 10.1007/s12220-012-9351-z. |
[8] |
F. Rampazzo and H. J. Sussmann, Set-valued differentials and a nonsmooth version of Chow-Rashevski's theorem, in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, December 2001, IEEE Publications, (2001), 2613-2618. |
[9] |
F. Rampazzo and H. J. Sussmann, Commutators of flow maps of nonsmooth vector fields, J. Differential Equations, 232 (2007), 134-175.
doi: 10.1016/j.jde.2006.04.016. |
[10] |
E. T. Sawyer and R. L. Wheeden, Hölder continuity of weak solutions to subelliptic equations with rough coefficients, Mem. Amer. Math. Soc., 180 (2006), x+157pp.
doi: 10.1090/memo/0847. |
[1] |
Linh V. Nguyen. A family of inversion formulas in thermoacoustic tomography. Inverse Problems and Imaging, 2009, 3 (4) : 649-675. doi: 10.3934/ipi.2009.3.649 |
[2] |
Takao Komatsu, Bijan Kumar Patel, Claudio Pita-Ruiz. Several formulas for Bernoulli numbers and polynomials. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021006 |
[3] |
Roderick S. C. Wong, H. Y. Zhang. On the connection formulas of the third Painlevé transcendent. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 541-560. doi: 10.3934/dcds.2009.23.541 |
[4] |
Jérôme Rousseau, Paulo Varandas, Yun Zhao. Entropy formulas for dynamical systems with mistakes. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4391-4407. doi: 10.3934/dcds.2012.32.4391 |
[5] |
J. C. Alvarez Paiva and E. Fernandes. Crofton formulas in projective Finsler spaces. Electronic Research Announcements, 1998, 4: 91-100. |
[6] |
Matthew B. Rudd. Statistical exponential formulas for homogeneous diffusion. Communications on Pure and Applied Analysis, 2015, 14 (1) : 269-284. doi: 10.3934/cpaa.2015.14.269 |
[7] |
Rui L. Fernandes, Yuxuan Zhang. Local and global integrability of Lie brackets. Journal of Geometric Mechanics, 2021, 13 (3) : 355-384. doi: 10.3934/jgm.2021024 |
[8] |
Dmitry Kleinbock, Barak Weiss. Dirichlet's theorem on diophantine approximation and homogeneous flows. Journal of Modern Dynamics, 2008, 2 (1) : 43-62. doi: 10.3934/jmd.2008.2.43 |
[9] |
Zvi Drezner, Carlton Scott. Approximate and exact formulas for the $(Q,r)$ inventory model. Journal of Industrial and Management Optimization, 2015, 11 (1) : 135-144. doi: 10.3934/jimo.2015.11.135 |
[10] |
Janusz Mierczyński, Wenxian Shen. Formulas for generalized principal Lyapunov exponent for parabolic PDEs. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1189-1199. doi: 10.3934/dcdss.2016048 |
[11] |
Paul Loya and Jinsung Park. On gluing formulas for the spectral invariants of Dirac type operators. Electronic Research Announcements, 2005, 11: 1-11. |
[12] |
Cuilian You, Le Bo. Option pricing formulas for generalized fuzzy stock model. Journal of Industrial and Management Optimization, 2020, 16 (1) : 387-396. doi: 10.3934/jimo.2018158 |
[13] |
João Paulo da Silva, Julio López, Ricardo Dahab. Isogeny formulas for Jacobi intersection and twisted hessian curves. Advances in Mathematics of Communications, 2020, 14 (3) : 507-523. doi: 10.3934/amc.2020048 |
[14] |
Francis N. Castro, Carlos Corrada-Bravo, Natalia Pacheco-Tallaj, Ivelisse Rubio. Explicit formulas for monomial involutions over finite fields. Advances in Mathematics of Communications, 2017, 11 (2) : 301-306. doi: 10.3934/amc.2017022 |
[15] |
Qing-Hu Hou, Yarong Wei. Telescoping method, summation formulas, and inversion pairs. Electronic Research Archive, 2021, 29 (4) : 2657-2671. doi: 10.3934/era.2021007 |
[16] |
Johannes Huebschmann. On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras. Journal of Geometric Mechanics, 2021, 13 (3) : 385-402. doi: 10.3934/jgm.2021009 |
[17] |
Matilde Martínez, Shigenori Matsumoto, Alberto Verjovsky. Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem. Journal of Modern Dynamics, 2016, 10: 113-134. doi: 10.3934/jmd.2016.10.113 |
[18] |
Michel L. Lapidus, Goran Radunović, Darko Žubrinić. Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces. Discrete and Continuous Dynamical Systems - S, 2019, 12 (1) : 105-117. doi: 10.3934/dcdss.2019007 |
[19] |
Tohru Wakasa, Shoji Yotsutani. Representation formulas for some 1-dimensional linearized eigenvalue problems. Communications on Pure and Applied Analysis, 2008, 7 (4) : 745-763. doi: 10.3934/cpaa.2008.7.745 |
[20] |
Stefan Erickson, Michael J. Jacobson, Jr., Andreas Stein. Explicit formulas for real hyperelliptic curves of genus 2 in affine representation. Advances in Mathematics of Communications, 2011, 5 (4) : 623-666. doi: 10.3934/amc.2011.5.623 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]