What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Geometry
Gérard Iooss mainly investigates Mathematical analysis, Classical mechanics, Bifurcation, Nonlinear system and Bifurcation theory.
His Mathematical analysis research includes themes of Dynamical systems theory, Vector field and Homogeneous space.
His study looks at the relationship between Bifurcation and topics such as Coupling, which overlap with Point, Structure and Phase.
His biological study spans a wide range of topics, including Turbulence, K-epsilon turbulence model and Reynolds decomposition.
His research integrates issues of Saddle-node bifurcation and Bifurcation diagram in his study of Bifurcation theory.
The various areas that Gérard Iooss examines in his Bifurcation diagram study include Nonlinear operators and Period-doubling bifurcation.
His most cited work include:
- Elementary stability and bifurcation theory (1024 citations)
- A simple global characterization for normal forms of singular vector fields (377 citations)
- The Couette-Taylor problem (334 citations)
What are the main themes of his work throughout his whole career to date?
Gérard Iooss mainly focuses on Mathematical analysis, Bifurcation, Classical mechanics, Bifurcation theory and Center manifold.
Specifically, his work in Mathematical analysis is concerned with the study of Partial differential equation.
His work in Bifurcation addresses issues such as Torus, which are connected to fields such as Invariant.
His Classical mechanics research integrates issues from Amplitude, Mechanics and Longitudinal wave.
While the research belongs to areas of Bifurcation theory, he spends his time largely on the problem of Flow, intersecting his research to questions surrounding Gravitational wave.
His Center manifold research incorporates elements of Invariant manifold and Ordinary differential equation.
He most often published in these fields:
- Mathematical analysis (62.88%)
- Bifurcation (25.76%)
- Classical mechanics (16.67%)
What were the highlights of his more recent work (between 2004-2021)?
- Mathematical analysis (62.88%)
- Classical mechanics (16.67%)
- Quasiperiodic function (6.82%)
In recent papers he was focusing on the following fields of study:
Gérard Iooss mostly deals with Mathematical analysis, Classical mechanics, Quasiperiodic function, Swift–Hohenberg equation and Invariant.
In general Mathematical analysis study, his work on Partial differential equation often relates to the realm of Complex system, thereby connecting several areas of interest.
His Classical mechanics research incorporates themes from Nonlinear theory, Nonlinear system, Clapotis and Eigenvalues and eigenvectors.
His work investigates the relationship between Swift–Hohenberg equation and topics such as Divisor that intersect with problems in Type, Fluid mechanics and Ordinary differential equation.
He combines subjects such as Linear subspace, Analytic manifold, Manifold, Invariant manifold and Vector field with his study of Invariant.
His Amplitude research includes elements of Infinity and Bifurcation theory.
Between 2004 and 2021, his most popular works were:
- Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (129 citations)
- Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity (106 citations)
- Localized waves in nonlinear oscillator chains (68 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Geometry
His primary areas of study are Mathematical analysis, Nonlinear system, Asymptotic expansion, Perfect fluid and Differential equation.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Bifurcation theory, Bifurcation, Classical mechanics, Surface and Gravitational wave.
His Bifurcation theory research is multidisciplinary, relying on both Invertible matrix, Quadratic equation, Gravity wave, Change of variables and Scalar.
Gérard Iooss interconnects Breather, Center manifold, Principal part, Ordinary differential equation and Homoclinic orbit in the investigation of issues within Classical mechanics.
His work on Linearization as part of general Nonlinear system research is frequently linked to Trigonometric polynomial, bridging the gap between disciplines.
His Differential equation research is multidisciplinary, incorporating elements of Discretization, Integrable system, Mathematical physics and Eigenvalues and eigenvectors.
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