zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Controllability of a nonholonomic macroeconomic system. (English) Zbl 1257.49022
Summary: This paper studies optimal control problems and sub-Riemannian geometry on a nonholonomic macroeconomic system. The main results show that a nonholonomic macroeconomic system is controllable either by trajectories of a single-time driftless control system (single-time bang-bang controls), or by nonholonomic geodesics or by sheets of a two-time driftless control system (two-time bang-bang controls). They are strongly connected to the possibility of describing a nonholonomic macroeconomic system via a Gibbs-Pfaff equation or by four associated vector fields, based on a contact structure of the state space and our isomorphism between thermodynamics and macroeconomics that praises three laws of a nonholonomic macroeconomic system.
49K30Optimal solutions belonging to restricted classes
53C17Sub-Riemannian geometry
91B64Macro-economic models (monetary models, models of taxation)
[1]Udrişte, C.: Thermodynamics versus economics. UPB Sci. Bull, Series A 69(3), 89–91 (2007)
[2]Udrişte, C., Ferrara, M., Zugrăvescu, D., Munteanu, F.: Geobiodynamics and Roegen type economy. Far East J. Math. Sci. (FJMS) 28(3), 681–693 (2008)
[3]Udrişte, C.: Geometric Dynamics. Kluwer, Amsterdam (2000)
[4]Udrişte, C., Dogaru, O., Ţevy, I.: Extrema with Nonholonomic Constraints. Monographs and Textbooks, vol. 4. Geometry Balkan Press, Bucharest (2002)
[5]Udrişte, C., Ferrara, M., Opriş, D.: Economic Geometric Dynamics. Monographs and Textbooks, vol. 6. Geometry Balkan Press, Bucharest (2004)
[6]Udrişte, C., Ferrara, M.: Black hole models in economics. Tensor NS 70(1), 53–62 (2008)
[7]Stamin, C., Udrişte, C.: Nonholonomic geometry of Gibbs contact structure. U.P.B. Sci. Bull., Series A 72(1), 153–170 (2010)
[8]Liu, W., Sussmann, H.: Abnormal sub-Riemannian minimizers. IMA Preprint Series # 1059 (1992)
[9]Udrişte, C.: Multitime controllability, observability and bang–bang principle. J. Optim. Theory Appl. 139(1), 141–157 (2008) · Zbl 1156.93013 · doi:10.1007/s10957-008-9430-2
[10]Udrişte, C.: Simplified multitime maximum principle. Balkan J. Geom. Appl. 14(1), 102–119 (2009)
[11]Udrişte, C.: Nonholonomic approach of multitime maximum principle. Balkan J. Geom. Appl. 14(2), 111–126 (2009)
[12]Udrişte, C., Ţevy, I.: Multitime linear-quadratic regulator problem based on curvilinear integral. Balkan J. Geom. Appl. 14(2), 127–137 (2009)
[13]Udrişte, C., Ţevy, I.: Multitime dynamic programming for curvilinear integral actions. J. Optim. Theory Appl. 146(1), 189–207 (2010) · Zbl 1202.49027 · doi:10.1007/s10957-010-9664-7
[14]Udrişte, C.: Equivalence of multitime optimal control problems. Balkan J. Geom. Appl. 15(1), 155–162 (2010)
[15]Udrişte, C.: Multitime maximum principle for curvilinear integral cost. Balkan J. Geom. Appl. 16(1), 128–149 (2011)
[16]Udrişte, C., Bejenaru, A.: Multitime optimal control with area integral costs on boundary. Balkan J. Geom. Appl. 16(2), 138–154 (2011)
[17]ShankarSastry, S., Montgomery, R.: The structure of optimal controls for steering problem. In: NOLCOS, Conf Proc., Bordeaux, France (1992)
[18]Chernavski, D.S., Starkov, N.I., Shcherbakov, A.V.: On some problems of physical economics. Phys. Usp. 45(9), 977–997 (2002) · doi:10.1070/PU2002v045n09ABEH001132
[19]Georgescu-Roegen, N.: The Entropy Law and Economic Process. Harvard University Press, Cambridge (1971)
[20]Ruth, M.: Insights from thermodynamics for the analysis of economic processes. In: Kleidon, A., Lorenz, R. (eds.) Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond, pp. 243–254. Springer, Heidelberg (2005)
[21]Smulders, S.: Entropy, environment and endogenous economic growth. Journal of International Tax and Public Finance 2, 317–338 (1995)
[22]Sergeev, V.: The thermodynamical approach to market (translated from Russian and edited by Leites, D.). Max Planck Institute, Preprint no: 76, (2006); arXiv:0803.3432v1 [physics.soc-ph] 24 Mar (2008)
[23]Nardini, F.: Technical Progress and Economic Growth. Springer, Berlin (2001)
[24]Vrănceanu, G.: Lectures of Differential Geometry Vol. I (in Romanian). Didactical and Pedagogical Editorial House, Bucharest (1962). Vol. II, (1964)