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At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I-VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these "nonlinear special functions". The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Pa

There are a number of intriguing connections between Painlevé equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlevé equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlevé transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlevé equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlevé equations.

The first book on pioneering French filmmaker Jean Painlevé, the father of science cinema.One of the first to plunge underwater with a camera to bring the subaquatic world to the screen, maverick scientific documentary filmmaker Jean Painlevé (1902-1989) captured the throes of a male seahorse giving birth, the geometric choreography of crystal formation, and the mating habits of hermaphrodite mollusks. In a lifetime spanning nearly the history of cinema itself, Painlevé made over 200 films, including The Seahorse, Freshwater Assassins, The Vampire, and The Love Life of the Octopus. His lyrical and instructive animal behavior films set to avant-garde scores were much admired by Surrealist contemporaries such as Antonin Artaud, Luis Buñuel, and Jean Vigo.Science Is Fiction includes Marina McDougall's historically informative "Hybrid Roots," Brigitte Berg's heavily illustrated biographical essay "Contradictory Forces," art critic Ralph Rugoff's "Fluid Mechanics," a Libération interview with Painlevé, stills from Painlevé's most celebrated films laid out in storyboard fashion, and a selection of Painlevé's writings appearing for the first time in English. The latter include "Neo-Zoological Drama," a playful romp on the behavior of Turbellaria, or flatworms; "Mysteries and Miracles of Nature," an idiosyncratic catalog of unusual animal behavior; and "Scientific Film," a discussion of science films that pays homage to Painlevé's fellow pioneers. The book also includes French film critic André Bazin's "Science Film: Accidental Beauty," a review of the 1947 International Association of Science Film festival, organized by Painlevé.Copublished with Brico Press.

An archive-based, in-depth analysis of the surreal nature and science movies of the pioneering French filmmaker Jean PainlevéBefore Jacques-Yves Cousteau, there was Jean Painlevé, a pioneering French scientific and nature filmmaker with a Surrealist’s eye. Creator of more than two hundred films, his studies of strange animal worlds doubled as critical reimaginations of humanity. With an unerring eye for the uncanny and unexpected, Painlevé and his assistant Geneviève Hamon captured oneiric octopuses, metamorphic crustaceans, erotic seahorses, mythic vampire bats, and insatiable predatory insects. Zoological Surrealism draws from Painlevé’s early oeuvre to rethink the entangled histories of cinema, Surrealism, and scientific research in interwar France. Delving deeply into Painlevé’s archive, James Leo Cahill develops an account of “cinema’s Copernican vocation”—how it was used to forge new scientific discoveries while also displacing and critiquing anthropocentric viewpoints. From Painlevé’s engagements with Sergei Eisenstein, Georges Franju, and competing Surrealists to the historiographical dimensions of Jean Vigo’s concept of social cinema, Zoological Surrealism taps never-before-examined sources to offer a completely original perspective on a cutting-edge filmmaker. The first extensive English-language study of Painlevé’s early films and their contexts, it adds important new insight to our understanding of film while also contributing to contemporary investigations of the increasingly surreal landscapes of climate change and ecological emergency.

The first book on pioneering French filmmaker Jean Painlevé, the father of science cinema.One of the first to plunge underwater with a camera to bring the subaquatic world to the screen, maverick scientific documentary filmmaker Jean Painlevé (1902-1989) captured the throes of a male seahorse giving birth, the geometric choreography of crystal formation, and the mating habits of hermaphrodite mollusks. In a lifetime spanning nearly the history of cinema itself, Painlevé made over 200 films, including The Seahorse, Freshwater Assassins, The Vampire, and The Love Life of the Octopus. His lyrical and instructive animal behavior films set to avant-garde scores were much admired by Surrealist contemporaries such as Antonin Artaud, Luis Buñuel, and Jean Vigo.Science Is Fiction includes Marina McDougall's historically informative "Hybrid Roots," Brigitte Berg's heavily illustrated biographical essay "Contradictory Forces," art critic Ralph Rugoff's "Fluid Mechanics," a Libération interview with Painlevé, stills from Painlevé's most celebrated films laid out in storyboard fashion, and a selection of Painlevé's writings appearing for the first time in English. The latter include "Neo-Zoological Drama," a playful romp on the behavior of Turbellaria, or flatworms; "Mysteries and Miracles of Nature," an idiosyncratic catalog of unusual animal behavior; and "Scientific Film," a discussion of science films that pays homage to Painlevé's fellow pioneers. The book also includes French film critic André Bazin's "Science Film: Accidental Beauty," a review of the 1947 International Association of Science Film festival, organized by Painlevé.Copublished with Brico Press.

The first book on pioneering French filmmaker Jean Painlevé, the father of science cinema.One of the first to plunge underwater with a camera to bring the subaquatic world to the screen, maverick scientific documentary filmmaker Jean Painlevé (1902-1989) captured the throes of a male seahorse giving birth, the geometric choreography of crystal formation, and the mating habits of hermaphrodite mollusks. In a lifetime spanning nearly the history of cinema itself, Painlevé made over 200 films, including The Seahorse, Freshwater Assassins, The Vampire, and The Love Life of the Octopus. His lyrical and instructive animal behavior films set to avant-garde scores were much admired by Surrealist contemporaries such as Antonin Artaud, Luis Buñuel, and Jean Vigo.Science Is Fiction includes Marina McDougall's historically informative "Hybrid Roots," Brigitte Berg's heavily illustrated biographical essay "Contradictory Forces," art critic Ralph Rugoff's "Fluid Mechanics," a Libération interview with Painlevé, stills from Painlevé's most celebrated films laid out in storyboard fashion, and a selection of Painlevé's writings appearing for the first time in English. The latter include "Neo-Zoological Drama," a playful romp on the behavior of Turbellaria, or flatworms; "Mysteries and Miracles of Nature," an idiosyncratic catalog of unusual animal behavior; and "Scientific Film," a discussion of science films that pays homage to Painlevé's fellow pioneers. The book also includes French film critic André Bazin's "Science Film: Accidental Beauty," a review of the 1947 International Association of Science Film festival, organized by Painlevé.Copublished with Brico Press.