D-Index & Metrics Best Publications

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 41 Citations 19,932 147 World Ranking 1240 National Ranking 569

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

1964 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Geometry
  • Topology

His scientific interests lie mostly in Pure mathematics, Discrete mathematics, Combinatorics, Dynamical systems theory and Mathematical analysis. Morris W. Hirsch combines subjects such as Fictitious play, Distribution, Partial differential equation and Ordinary differential equation with his study of Pure mathematics. Morris W. Hirsch works mostly in the field of Partial differential equation, limiting it down to topics relating to Class and, in certain cases, State, as a part of the same area of interest.

His Ordinary differential equation research is multidisciplinary, relying on both Stability, Mathematical economics and Monotone polygon. His Discrete mathematics study combines topics from a wide range of disciplines, such as Space, Vector field and Algebra. His Dynamical systems theory study combines topics in areas such as Ignorance and Human intelligence.

His most cited work include:

    1. Monotone Dynamical Systems (646 citations)
  • Convergent activation dynamics in continuous time networks (541 citations)
  • Stable manifolds for hyperbolic sets (395 citations)

What are the main themes of his work throughout his whole career to date?

Morris W. Hirsch focuses on Pure mathematics, Mathematical analysis, Discrete mathematics, Dynamical systems theory and Combinatorics. In his research, Morris W. Hirsch undertakes multidisciplinary study on Pure mathematics and Affine representation. His Discrete mathematics research includes elements of Point, Schwarzian derivative, Periodic orbits and Algebra.

As part of the same scientific family, Morris W. Hirsch usually focuses on Dynamical systems theory, concentrating on Artificial neural network and intersecting with Computation. His studies deal with areas such as Manifold, Hyperbolic set, Diffeomorphism and Submanifold as well as Combinatorics. Morris W. Hirsch interconnects Space and Euclidean space in the investigation of issues within Affine transformation.

He most often published in these fields:

  • Pure mathematics (43.48%)
  • Mathematical analysis (18.48%)
  • Discrete mathematics (19.57%)

What were the highlights of his more recent work (between 2001-2016)?

  • Pure mathematics (43.48%)
  • Lie group (9.78%)
  • Mathematical economics (6.52%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Pure mathematics, Lie group, Mathematical economics, Discrete mathematics and Monotone polygon. As a part of the same scientific family, Morris W. Hirsch mostly works in the field of Mathematical economics, focusing on Dynamical systems theory and, on occasion, Dynamical system and Differential equation. His studies in Discrete mathematics integrate themes in fields like Schwarzian derivative, Point, Interval and Calculus.

His study in Monotone polygon is interdisciplinary in nature, drawing from both Class, Partial differential equation and Compact space. His Partial differential equation study is associated with Mathematical analysis. The Stability study which covers Ordinary differential equation that intersects with State.

Between 2001 and 2016, his most popular works were:

    1. Monotone Dynamical Systems (646 citations)
  • Monotone maps: a review (100 citations)
  • Chapter 4 Monotone Dynamical Systems (81 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Geometry
  • Topology

Morris W. Hirsch mostly deals with Monotone polygon, Mathematical economics, Class, Dynamical systems theory and Partial differential equation. His work carried out in the field of Monotone polygon brings together such families of science as Discrete mathematics and Algebra. His Class study incorporates themes from State space, Ordinary differential equation and Monotone dynamical system.

The Dynamical systems theory study combines topics in areas such as Dynamical system and Differential equation. His research in Partial differential equation intersects with topics in Stability, State and Compact space, Pure mathematics. His Pure mathematics study integrates concerns from other disciplines, such as Equilibrium set and Order.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Morris W. Hirsch;Stephen Smale;Robert L. Devaney.
(2003)

5705 Citations

Differential Equations, Dynamical Systems, and Linear Algebra

Morris W. Hirsch;Stephen Smale.
(1974)

3973 Citations

Immersions of manifolds

Morris W. Hirsch.
Transactions of the American Mathematical Society (1959)

812 Citations

Convergent activation dynamics in continuous time networks

M. W. Hirsch.
Neural Networks (1989)

784 Citations

Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere

Morris W. Hirsch.
Siam Journal on Mathematical Analysis (1985)

707 Citations

4. Monotone Dynamical Systems

Morris W Hirsch;Hal Smith.
(2005)

657 Citations

Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets

Morris W. Hirsch.
Siam Journal on Mathematical Analysis (1982)

635 Citations

Stable manifolds for hyperbolic sets

Morris W. Hirsch;Charles C. Pugh.
Bulletin of the American Mathematical Society (1969)

612 Citations

Stability regions of nonlinear autonomous dynamical systems

H.-D. Chiang;M.W. Hirsch;F.F. Wu.
IEEE Transactions on Automatic Control (1988)

609 Citations

Stability and convergence in strongly monotone dynamical systems.

Morris W. Hirsch.
Crelle's Journal (1988)

494 Citations

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