mathematics

Henri Dulac

Henri Dulac is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Henri Dulac rather than just read about it. In short: Henri Claudius Marie Rosario Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician. Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Mathematics.

Key takeaways

Henri Dulac belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Henri Dulac to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Henri Dulac from memory before moving on to harder problems.

Reference excerpt

Henri Claudius Marie Rosario Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician.

Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Mathematics. He started to teach a class of mathematic analysis at University, in Grenoble (France), Algiers (today Algeria) and Poitiers (France). Holder of a pulpit in pure mathematics in the Sciences University of Lyon (France) in 1911, his teaching was suspended during the First World War (1914 – 1918) and he had to serve as officer in the French army. After the war, he became holder of a pulpit of differential and integral calculus and also taught in École Centrale Lyon. He became examiner at École Polytechnique (Paris) and President of the admission jury. Awarded Officer of Legion d'honneur, the French order established by Napoleon and associate member of the French Academy of Sciences, he published part of Euler's works and contributed to the research through many publications in France and abroad. Father of 3 children, Anie (1901–1935), bachelor in mathematics, Jean (1903–2005), graduate of École Polytechnique, 1921 and Robert (1904–1996), graduate of polytechnique, 1922; he died in Fayence, France, in 1955.

Work Among his publications:

Recherches sur les points singuliers des équations différentielles (Journal of École Polytechnique, 1904). Intégrales d'une équation différentielle (Annales University of Grenoble, 1905). Sur les Points dicritiques (Journal of mathématics, 1906). Sur les séries de Mac-Laurin à plusieurs variables (Acta Mathematica, 1906). Détermination et intégration d'une classe d'équations différentielles (Bulletin of mathematical sciences). Intégrales passant par un point singulier (Rendeconti del Circolo, 1911). Sur les points singuliers (Annales, Toulouse, 1912). Solutions d'un système d'équations différentielles (Bulletin of the mathematical society, 1913). Sur les cycles limites (Bulletin of the mathematical society, 1923). Points singuliers des équations différentielles (Mémorial des sciences mathématiques, 1932). Courbes définies par une équation différentielle du premier ordre (Mémorial des sciences mathématiques, 1934). His researches are still mentioned or challenged by international university PHD students and professors, even a hundred years after being published. As an example:

The Center Variety of Polynomial Differential Systems – Abdu Salam Jarrah, Faculté des sciences mathématiques, Université du Nouveau Mexique, USA (2001). Complete Polynomial Vector Fields on C2 – Julio Rebelo, Institute for Mathematical Sciences, SUNY, New York, USA (Oct. 2002). Dimension Increase and Splitting for Poincaré-Dulac Normal forms – Giuseppe Gaeta, Faculté de Mathématique de l'Université de Milan and Sebastian Walcher, chaire de Mathématique, Aix La Chapelle, Journal of Non linear Mathematical Physices (2005). Sources: Technica, n° 190, Nov. 1955, École Centrale Lyon, French Academy of Sciences, updated by Louis Boisgibault, his great grandson.

See also Bendixson–Dulac theorem Hilbert's sixteenth problem Transseries

References

External links Works by or about Henri Dulac at the Internet Archive

Illustrations

Worked examples

Example 1 — a first encounter with Henri Dulac

Start with the simplest possible case. Write down what Henri Dulac claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Henri Dulac before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Henri Dulac ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Henri Dulac

In research: Henri Dulac appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Henri Dulac in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Henri Dulac is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1870 births, 1955 deaths, French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henri Dulac outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Henri Dulac in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henri Dulac means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Henri Dulac out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henri Dulac in simple terms?

Henri Claudius Marie Rosario Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician. Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Mathematics.

Why does Henri Dulac matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Henri Dulac?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Henri Dulac.