# Some families of pseudo-processes

Annales Polonici Mathematici (1994)

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

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topJ. 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

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

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