Some families of pseudo-processes

J. Kłapyta

Annales Polonici Mathematici (1994)

  • Volume: 60, Issue: 1, page 33-45
  • ISSN: 0066-2216

Abstract

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We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space ℝ m . The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.

How to cite

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J. Kłapyta. "Some families of pseudo-processes." Annales Polonici Mathematici 60.1 (1994): 33-45. <http://eudml.org/doc/262489>.

@article{J1994,
abstract = {We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space $ℝ^m$. The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.},
author = {J. Kłapyta},
journal = {Annales Polonici Mathematici},
keywords = {topological dynamics; dispersiveness; unstability; stability; Poisson unstable pseudo-processes; Lagrange unstable pseudo-processes},
language = {eng},
number = {1},
pages = {33-45},
title = {Some families of pseudo-processes},
url = {http://eudml.org/doc/262489},
volume = {60},
year = {1994},
}

TY - JOUR
AU - J. Kłapyta
TI - Some families of pseudo-processes
JO - Annales Polonici Mathematici
PY - 1994
VL - 60
IS - 1
SP - 33
EP - 45
AB - We introduce several types of notions of dis persive, completely unstable, Poisson unstable and Lagrange uns table pseudo-processes. We try to answer the question of how many (in the sense of Baire category) pseudo-processes with each of these properties can be defined on the space $ℝ^m$. The connections are discussed between several types of pseudo-processes and their limit sets, prolongations and prolongational limit sets. We also present examples of applications of the above results to pseudo-processes generated by differential equations.
LA - eng
KW - topological dynamics; dispersiveness; unstability; stability; Poisson unstable pseudo-processes; Lagrange unstable pseudo-processes
UR - http://eudml.org/doc/262489
ER -

References

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  1. [1] N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer, Berlin, 1970. 
  2. [2] C. M. Dafermos, An invariant principle for compact processes, J. Differential Equations 9 (1971), 239-252. 
  3. [3] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  4. [4] R. C. Haworth and R. A. McCoy, Baire spaces, Dissertationes Math. 141 (1977). Zbl0344.54001
  5. [5] J. Kłapyta, A classification of dynamical systems, Ann. Polon. Math. 53 (1991), 109-121. Zbl0739.54020
  6. [6] A. Pelczar, Stability questions in generalized processes and in pseudo-dynamical systems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom Phys. 21 (1973), 541-549. Zbl0268.54046
  7. [7] A. Pelczar, Limit sets and prolongations in pseudo-processes, Univ. Iagell. Acta Math. 27 (1988), 169-186. Zbl0675.54038
  8. [8] A. Pelczar, General Dynamical Systems, Monographs of the Jagiellonian University, No. 293, Kraków, 1978 (in Polish). 
  9. [9] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967. 

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