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Topic · Mathematical Physics

Mathematical Dynamics and Fractals

Mathematical Dynamics and Fractals is a research topic within Mathematical Physics. Science Explorer counts 31k research works in it since 1950. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in dynamical systems and chaos theory, including chaos implications, ergodic theory, fractals, Lyapunov exponents, Markov chains, topological entropy, invariant measures, Teichmüller curves, and Hausdorff dimension.

  • Chaos
  • Dynamical Systems
  • Fractals
  • Ergodic Theory
  • Lyapunov Exponents
  • Markov Chains
  • Topological Entropy
  • Invariant Measures
  • Teichmüller Curves
  • Hausdorff Dimension
Research works
31k
fractional, since 1950
In the world top 10%
3.2k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+16%
the tick is no change
Largest producer
China
25% of the 10 largest, 2022-now
Mathematical Dynamics and Fractals

Which countries lead Mathematical Dynamics and Fractals research?

By volume, China and the United States publish the most (737 and 641 works in 2022-now).

By volume, 2022-now

  1. 1 China 737 works
  2. 2 United States 641 works
  3. 3 France 326 works
  4. 4 Russia 253 works
  5. 5 India 229 works
  6. 6 United Kingdom 176 works
  7. 7 Japan 151 works
  8. 8 Brazil 145 works
  9. 9 Germany 134 works
  10. 10 Italy 104 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 25.5%United States: 22.1%France: 11.3%Russia: 8.7%6 others listed: 32.4%25%largest
China737 · 25.5%United States641 · 22.1%France326 · 11.3%Russia253 · 8.7%6 others listed939 · 32.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Mathematical Dynamics and Fractals research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Mathematical Dynamics and Fractals research, followed by National Research University Higher School of Economics and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 162 works
  2. 2 National Research University Higher School of EconomicsRussia 58 works
  3. 3 Russian Academy of SciencesRussia 49 works
  4. 4 Lomonosov Moscow State UniversityRussia 31 works
  5. 5 Chongqing UniversityChina 23 works
  6. 6 South China University of TechnologyChina 21 works
  7. 7 University of WarwickUnited Kingdom 20 works
  8. 8 Nanjing University of Science and TechnologyChina 19 works
  9. 9 Polish Academy of SciencesPoland 19 works
  10. 10 University of MonastirTunisia 18 works

Who are the leading researchers in Mathematical Dynamics and Fractals?

The most-cited researchers publishing on Mathematical Dynamics and Fractals include Zhong Lin Wang, David H. Haussler and Harry Eugene Stanley.

  1. 1 Zhong Lin Wang United States 491k citations
  2. 2 David H. Haussler United States 209k citations
  3. 3 Harry Eugene Stanley United States 198k citations
  4. 4 R. W. L. Jones United Kingdom 189k citations
  5. 5 Peter Donnelly United Kingdom 175k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Mathematical Dynamics and Fractals?

The most cited paper in Mathematical Dynamics and Fractals is "Measuring the strangeness of strange attractors" (Peter Grassberger, Itamar Procaccia, 1983), with 5,689 citations. Next come "Ergodic theory of chaos and strange attractors" (4,989) and "An equation for continuous chaos" (4,050).

Most cited papers
#PaperReleasedCitations
1 Measuring the strangeness of strange attractors Peter Grassberger, Itamar Procaccia · Physica D Nonlinear Phenomena Oct 1983 5,689
2 Ergodic theory of chaos and strange attractors Jean‐Pierre Eckmann, David Pierre Ruelle · Reviews of Modern Physics Jul 1985 4,989
3 An equation for continuous chaos Otto E. Rössler · Physics Letters A Jul 1976 4,050
4 Differentiable Dynamical Systems Steve Smale Book chapter 1980 2,543
5 An Introduction to Chaotic Dynamical Systems Robert L. Devaney, Jean‐Pierre Eckmann · Physics Today Jul 1987 2,385
All 100 most cited papers, with filters and sorting

Where is Mathematical Dynamics and Fractals research done?

The largest centres of Mathematical Dynamics and Fractals research in 2022-now are Moscow (Russia), Paris (France), Beijing (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Coventry.

Largest cities, 2022-now

  1. 1 MoscowRussia 152 works
  2. 2 ParisFrance 114 works
  3. 3 BeijingChina 72 works
  4. 4 NanjingChina 64 works
  5. 5 GuangzhouChina 62 works
  6. 6 TokyoJapan 51 works
  7. 7 WuhanChina 44 works
  8. 8 ShanghaiChina 44 works
  9. 9 ChongqingChina 34 works
  10. 10 New YorkUnited States 33 works

Where it is the local speciality

  1. CoventryGB · 20.5 works8.1×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Mathematical Dynamics and Fractals than the world average.

See Mathematical Dynamics and Fractals on the map

Where is the best place to study Mathematical Dynamics and Fractals?

Among universities, judged by research, University of Monastir, National Research University Higher School of Economics and Nanjing University of Science and Technology score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 21.29%fractional works in this field (log) →share of work in the world top 10% →University of MonastirNorthwest UniversityNanjing University o…National Research Un…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of MonastirTunisia 80.045.5%33.5×18 +15.0%
2National Research University Higher School of EconomicsRussia 54.84.7%39.7×58 +19.8%
3Nanjing University of Science and TechnologyChina 54.725.1%6.6×19 +250.6%
4Northwest UniversityChina 52.444.3%9.0×10 +59.6%
5Chongqing UniversityChina 51.717.1%6.0×23 +177.0%
6University of Maryland, College ParkUnited States 49.515.9%7.7×16 +78.0%
7University of WarwickUnited Kingdom 47.54.0%12.3×20 +36.9%
8Université Paris-SaclayFrance 47.210.4%7.7×18 +119.5%
9Yale UniversityUnited States 45.330.3%2.6×10 +101.2%
10Massachusetts Institute of TechnologyUnited States 44.915.6%4.9×12 +19.9%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Mathematical Dynamics and Fractals, country by country

Is Mathematical Dynamics and Fractals research growing?

Output in 2022-2025 was 16% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Mathematical Dynamics and Fractals.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Mathematical Dynamics and Fractals as a percentage of every work published that year, 0.017% in 2024.

still counting0.020%0.040%0.060%Mathematical Dynamics and Fractals0.017% in 202519801990200020102020

Fractional works of Mathematical Dynamics and Fractals over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Mathematical Dynamics and Fractals10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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