Philippe Bolle

870 total citations
23 papers, 469 citations indexed

About

Philippe Bolle is a scholar working on Statistical and Nonlinear Physics, Mathematical Physics and Numerical Analysis. According to data from OpenAlex, Philippe Bolle has authored 23 papers receiving a total of 469 indexed citations (citations by other indexed papers that have themselves been cited), including 20 papers in Statistical and Nonlinear Physics, 8 papers in Mathematical Physics and 6 papers in Numerical Analysis. Recurrent topics in Philippe Bolle's work include Quantum chaos and dynamical systems (19 papers), Nonlinear Waves and Solitons (8 papers) and Nonlinear Photonic Systems (5 papers). Philippe Bolle is often cited by papers focused on Quantum chaos and dynamical systems (19 papers), Nonlinear Waves and Solitons (8 papers) and Nonlinear Photonic Systems (5 papers). Philippe Bolle collaborates with scholars based in France, Italy and Switzerland. Philippe Bolle's co-authors include Massimiliano Berti, Luca Biasco, Michela Procesi, Massimiliano Berti and B. Buffoni and has published in prestigious journals such as Archive for Rational Mechanics and Analysis, Journal of Differential Equations and Advances in Mathematics.

In The Last Decade

Philippe Bolle

23 papers receiving 409 citations

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
Philippe Bolle France	12	357	178	132	95	57	23	469
Sergei Kuksin France	9	310 0.9×	197 1.1×	83 0.6×	78 0.8×	22 0.4×	12	504
Luca Biasco Italy	9	315 0.9×	113 0.6×	116 0.9×	17 0.2×	33 0.6×	37	409
Richard C. Churchill United States	13	360 1.0×	143 0.8×	47 0.4×	32 0.3×	168 2.9×	32	451
Helmut Rüßmann Germany	9	231 0.6×	142 0.8×	42 0.3×	44 0.5×	94 1.6×	15	311
J�rgen Moser United States	5	336 0.9×	131 0.7×	62 0.5×	27 0.3×	102 1.8×	6	452
Ugo Bessi Italy	10	158 0.4×	95 0.5×	34 0.3×	81 0.9×	54 0.9×	26	269
Dmitrii Valer'evich Treschev Russia	10	265 0.7×	124 0.7×	21 0.2×	26 0.3×	63 1.1×	28	329
S. Duzhin Russia	6	250 0.7×	133 0.7×	63 0.5×	40 0.4×	209 3.7×	21	418
Jean-Pierre Ramis France	13	231 0.6×	190 1.1×	91 0.7×	220 2.3×	396 6.9×	25	672
Jordi Villanueva Spain	11	349 1.0×	130 0.7×	46 0.3×	11 0.1×	75 1.3×	24	427

Countries citing papers authored by Philippe Bolle

Since Specialization

Citations

This map shows the geographic impact of Philippe Bolle'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 Philippe Bolle with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Philippe Bolle more than expected).

Fields of papers citing papers by Philippe Bolle

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Philippe Bolle. 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 Philippe Bolle. The network helps show where Philippe Bolle may publish in the future.

Co-authorship network of co-authors of Philippe Bolle

This figure shows the co-authorship network connecting the top 25 collaborators of Philippe Bolle. A scholar is included among the top collaborators of Philippe Bolle 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 Philippe Bolle. Philippe Bolle 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

Berti, Massimiliano & Philippe Bolle. (2020). Quasi-Periodic Solutions of Nonlinear Wave Equations on the $d$-Dimensional Torus. 11 indexed citations

Berti, Massimiliano & Philippe Bolle. (2019). Quasi-periodic solutions of nonlinear wave equations on $T^d$. arXiv (Cornell University). 1 indexed citations

Bolle, Philippe, et al.. (2015). Tonelli Hamiltonians without conjugate points and $$C^0$$ C 0 integrability. Mathematische Zeitschrift. 280(1-2). 165–194. 3 indexed citations

Berti, Massimiliano & Philippe Bolle. (2012). Quasi-periodic solutions with Sobolev regularity of NLS on $\mathbb T^d$ with a multiplicative potential. Journal of the European Mathematical Society. 15(1). 229–286. 78 indexed citations

Berti, Massimiliano, Philippe Bolle, & Michela Procesi. (2009). An abstract Nash–Moser theorem with parameters and applications to PDEs. Annales de l Institut Henri Poincaré C Analyse Non Linéaire. 27(1). 377–399. 37 indexed citations

Berti, Massimiliano & Philippe Bolle. (2008). Cantor families of periodic solutions for wave equations via a variational principle. Advances in Mathematics. 217(4). 1671–1727. 8 indexed citations

Berti, Massimiliano & Philippe Bolle. (2008). Cantor families of periodic solutions for completely resonant wave equations. Frontiers of Mathematics in China. 3(2). 151–165. 1 indexed citations

Berti, Massimiliano & Philippe Bolle. (2006). Cantor families of periodic solutions for completely resonant nonlinear wave equations. Duke Mathematical Journal. 134(2). 45 indexed citations

Berti, Massimiliano & Philippe Bolle. (2004). Bifurcation of free vibrations for completely resonant wave equations. ArXiv.org. 7(2). 519–528. 1 indexed citations

10.

Berti, Massimiliano, Luca Biasco, & Philippe Bolle. (2003). Drift in phase space: a new variational mechanism with optimal diffusion time. Journal de Mathématiques Pures et Appliquées. 82(6). 613–664. 47 indexed citations

11.

Berti, Massimiliano & Philippe Bolle. (2003). Multiplicity of periodic solutions of nonlinear wave equations. Nonlinear Analysis. 56(7). 1011–1046. 31 indexed citations

12.

Berti, Massimiliano, Luca Biasco, & Philippe Bolle. (2002). Optimal stability and instability results for a class of nearly integrable Hamiltonian systems. ArXiv.org. 13(2). 77–84. 6 indexed citations

13.

Berti, Massimiliano & Philippe Bolle. (2002). A functional analysis approach to Arnold diffusion. Annales de l Institut Henri Poincaré C Analyse Non Linéaire. 19(4). 395–450. 33 indexed citations

14.

Berti, Massimiliano & Philippe Bolle. (2002). Fast Arnold diffusion in systems with three time scales. Discrete and Continuous Dynamical Systems. 8(3). 795–811. 11 indexed citations

15.

Berti, Massimiliano & Philippe Bolle. (2000). Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni. 11(4). 235–243. 9 indexed citations

16.

Bolle, Philippe. (1999). On the Bolza Problem. Journal of Differential Equations. 152(2). 274–288. 44 indexed citations

17.

Bolle, Philippe & B. Buffoni. (1999). Multibump homoclinic solutions to a centre equilibrium in a class of autonomous Hamiltonian systems. Nonlinearity. 12(6). 1699–1716. 5 indexed citations

18.

Berti, Massimiliano & Philippe Bolle. (1999). Homoclinics and chaotic behaviour for perturbed second order systems. Annali di Matematica Pura ed Applicata (1923 -). 176(1). 323–378. 21 indexed citations

19.

Berti, Massimiliano & Philippe Bolle. (1998). Variational Construction of Homoclinics and Chaos in Presence of a Saddle-Saddle Equilibrium. arXiv (Cornell University). 9(3). 167–175. 1 indexed citations

20.

Bolle, Philippe. (1998). A contact condition for $p$ -codimensional submanifolds of a symplectic manifold ( $2\leq p\leq n$ ). Mathematische Zeitschrift. 227(2). 211–230. 11 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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