Some families of pseudo-processes

• Autorzy: J. Kłapyta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

topological dynamics; dispersiveness; unstability; stability

Kategorie tematyczne

• 54H20: Topological dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 1
• Strony: 33-45

Daty

wydano

1994

otrzymano

1990-11-30

poprawiono

1992-02-20

poprawiono

1994-02-02

Twórcy

autor

J. Kłapyta

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [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).
• [5] J. Kłapyta, A classification of dynamical systems, Ann. Polon. Math. 53 (1991), 109-121.
• [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.
• [7] A. Pelczar, Limit sets and prolongations in pseudo-processes, Univ. Iagell. Acta Math. 27 (1988), 169-186.
• [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.