# Conservation laws and symmetry in economic growth models: a geometrical approach.

Manuel de León; David Martín de Diego

Extracta Mathematicae (1998)

- Volume: 13, Issue: 3, page 335-348
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topLeón, Manuel de, and Martín de Diego, David. "Conservation laws and symmetry in economic growth models: a geometrical approach.." Extracta Mathematicae 13.3 (1998): 335-348. <http://eudml.org/doc/38574>.

@article{León1998,

abstract = {The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian function is singular, which is usually the case in economic models. On the other hand, we apply our methods to derive some well-known conservation laws, in particular the income-wealth conservation law obtained by Weitzman (1976) and the Samuelson's first law (see Samuelson (1970)).},

author = {León, Manuel de, Martín de Diego, David},

journal = {Extracta Mathematicae},

keywords = {Sistemas mecánicos; Ecuaciones diferenciales; Ecuaciones de segundo orden; Crecimiento económico; Modelo geométrico; Sistema infinitesimal; Sistemas dinámicos; Lagrangian function; economic growth model; symplectic technique},

language = {eng},

number = {3},

pages = {335-348},

title = {Conservation laws and symmetry in economic growth models: a geometrical approach.},

url = {http://eudml.org/doc/38574},

volume = {13},

year = {1998},

}

TY - JOUR

AU - León, Manuel de

AU - Martín de Diego, David

TI - Conservation laws and symmetry in economic growth models: a geometrical approach.

JO - Extracta Mathematicae

PY - 1998

VL - 13

IS - 3

SP - 335

EP - 348

AB - The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian function is singular, which is usually the case in economic models. On the other hand, we apply our methods to derive some well-known conservation laws, in particular the income-wealth conservation law obtained by Weitzman (1976) and the Samuelson's first law (see Samuelson (1970)).

LA - eng

KW - Sistemas mecánicos; Ecuaciones diferenciales; Ecuaciones de segundo orden; Crecimiento económico; Modelo geométrico; Sistema infinitesimal; Sistemas dinámicos; Lagrangian function; economic growth model; symplectic technique

UR - http://eudml.org/doc/38574

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.