Patrick Bernard

1.1k total citations
36 papers, 513 citations indexed

About

Patrick Bernard is a scholar working on Statistical and Nonlinear Physics, Geometry and Topology and Mathematical Physics. According to data from OpenAlex, Patrick Bernard has authored 36 papers receiving a total of 513 indexed citations (citations by other indexed papers that have themselves been cited), including 19 papers in Statistical and Nonlinear Physics, 18 papers in Geometry and Topology and 15 papers in Mathematical Physics. Recurrent topics in Patrick Bernard's work include Quantum chaos and dynamical systems (17 papers), Mathematical Dynamics and Fractals (10 papers) and Advanced Differential Equations and Dynamical Systems (9 papers). Patrick Bernard is often cited by papers focused on Quantum chaos and dynamical systems (17 papers), Mathematical Dynamics and Fractals (10 papers) and Advanced Differential Equations and Dynamical Systems (9 papers). Patrick Bernard collaborates with scholars based in France, Burundi and Switzerland. Patrick Bernard's co-authors include Boris Buffoni, Jean‐Michel Roquejoffre, Richard D. Gill, Stanislav Molchanov, Dominique Bakry, M. Taazount, Ross W. Lambert, Michel Fogli, Eric Lombardi and Ugo Bessi and has published in prestigious journals such as IEEE Transactions on Power Delivery, Annals of Mathematics and Archive for Rational Mechanics and Analysis.

In The Last Decade

Patrick Bernard

35 papers receiving 479 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Patrick Bernard France	14	304	219	200	146	46	36	513
Ana Cannas da Silva United States	8	140 0.5×	319 1.5×	256 1.3×	67 0.5×	46 1.0×	11	542
Weiyuan Qiu China	13	191 0.6×	189 0.9×	128 0.6×	111 0.8×	24 0.5×	53	539
Amjad Hussain Pakistan	15	399 1.3×	163 0.7×	80 0.4×	205 1.4×	35 0.8×	58	767
Дмитрий Валерьевич Трещeв Russia	10	341 1.1×	176 0.8×	133 0.7×	57 0.4×	24 0.5×	27	503
J. A. C. Kolk Netherlands	8	58 0.2×	261 1.2×	162 0.8×	101 0.7×	14 0.3×	8	422
Andrew Russell Forsyth	3	161 0.5×	62 0.3×	81 0.4×	70 0.5×	40 0.9×	4	374
Reinhard Schäfke France	11	177 0.6×	96 0.4×	162 0.8×	168 1.2×	15 0.3×	48	460
Lee-Peng Teo Malaysia	17	373 1.2×	53 0.2×	116 0.6×	195 1.3×	274 6.0×	50	762
Jean-Pierre Ramis France	13	231 0.8×	190 0.9×	396 2.0×	220 1.5×	22 0.5×	25	672
Antonio Siconolfi Italy	11	181 0.6×	102 0.5×	114 0.6×	260 1.8×	53 1.2×	30	476

Countries citing papers authored by Patrick Bernard

Since Specialization

Citations

This map shows the geographic impact of Patrick Bernard's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Patrick Bernard with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Patrick Bernard more than expected).

Fields of papers citing papers by Patrick Bernard

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Patrick Bernard. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Patrick Bernard. The network helps show where Patrick Bernard may publish in the future.

Co-authorship network of co-authors of Patrick Bernard

This figure shows the co-authorship network connecting the top 25 collaborators of Patrick Bernard. A scholar is included among the top collaborators of Patrick Bernard based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Patrick Bernard. Patrick Bernard is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

Bernard, Patrick. (2024). Non-degeneracy of closed orbits for generic potentials. arXiv (Cornell University). 11. 363–393.

Bernard, Patrick, et al.. (2018). Smoothing causal functions. Journal of Physics Conference Series. 968. 12001–12001. 1 indexed citations

Bernard, Patrick, et al.. (2011). A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.. Mathematical Proceedings of the Cambridge Philosophical Society. 152(1). 167–178. 7 indexed citations

Bernard, Patrick. (2010). Lasry-Lions Regularization and a Lemma of Ilmanen. Rendiconti del Seminario Matematico della Università di Padova. 124. 221–229. 14 indexed citations

Bernard, Patrick, et al.. (2010). A GEOMETRIC DEFINITION OF THE AUBRY–MATHER SET. Journal of Topology and Analysis. 2(3). 385–393. 3 indexed citations

Bernard, Patrick. (2007). Smooth critical sub-solutions of the Hamilton-Jacobi equation. Mathematical Research Letters. 14(3). 503–511. 8 indexed citations

Bernard, Patrick, et al.. (2007). Asymptotic analysis of the random decrement. Probabilistic Engineering Mechanics. 22(3). 250–256. 6 indexed citations

Bernard, Patrick. (2007). Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds. Annales Scientifiques de l École Normale Supérieure. 40(3). 445–452. 52 indexed citations

Bernard, Patrick & Boris Buffoni. (2007). Optimal mass transportation and Mather theory. Journal of the European Mathematical Society. 9(1). 85–121. 62 indexed citations

10.

Bernard, Patrick & Boris Buffoni. (2006). The Monge problem for supercritical Mañé potentials on compact manifolds. Advances in Mathematics. 207(2). 691–706. 15 indexed citations

11.

Bernard, Patrick. (2003). The action spectrum near positive definite invariant tori. Bulletin de la Société mathématique de France. 131(4). 603–616. 6 indexed citations

12.

Bernard, Patrick. (2002). Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits. Journal of Differential Equations. 180(2). 427–452. 10 indexed citations

13.

Bernard, Patrick, et al.. (2002). Stochastic Newmark scheme. Probabilistic Engineering Mechanics. 17(1). 45–61. 14 indexed citations

14.

Bernard, Patrick. (2002). Connecting orbits of time dependent Lagrangian systems. Annales de l’institut Fourier. 52(5). 1533–1568. 44 indexed citations

15.

Bernard, Patrick. (2000). Homoclinic orbits to invariant sets of quasi-integrable exact maps. Ergodic Theory and Dynamical Systems. 20(6). 1583–1601. 15 indexed citations

16.

Bernard, Patrick. (1999). Another way of looking at fisheries management: the computable general equilibrium models. Agricultural economics research. 1 indexed citations

17.

Bernard, Patrick, et al.. (1999). Estimating the probability of failure of equipment as a result of direct lightning strikes on transmission lines. IEEE Transactions on Power Delivery. 14(4). 1394–1400. 8 indexed citations

18.

Bernard, Patrick, et al.. (1997). Asymptotic analysis and linearization of the randomly perturbed two-wells Duffing oscillator. Probabilistic Engineering Mechanics. 12(3). 171–178. 11 indexed citations

19.

Bernard, Patrick & M. Taazount. (1994). Random dynamics of structures with gaps: Simulation and spectral linearization. Nonlinear Dynamics. 5(3). 313–335. 6 indexed citations

20.

Bernard, Patrick, et al.. (1987). UNE METHODE DE MONTE-CARLO PERFORMANTE POUR LE CALCUL DE LA PROBABILITE DE RUINE. 4 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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