KLAUDIUSZ WÓJCIK HOMEPAGE


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RESEARCH INTEREST



dynamical systems - topological methods in dynamics - homology and dynamics - Ważewski retract method - isolated invariant sets - Conley index - fixed point index - Lefschetz numbers - Nielsen numbers - dynamics on surfaces - hyperbolic dynamics - invariant manifolds - attractors - bifurcations - chaos - entropy - topological horseshoes - symbolic dynamics - topological degree theory - critical point theory - nonlinear analysis - hamiltonian dynamics - Morse theory - algebraic topology - symplectic topology









"Fixed point results based on Ważewski method"

published in

"Handbook of topological fixed point theory"


Ed: R. Brown, M. Furi, L. Gorniewicz, B. Jiang,
Springer 2005, 903-941

(co-authors Roman Srzednicki, and Piotr Zgliczyński,)






SELECTED PUBLISHED PAPERS




CHAOTIC DYNAMICS


"Periodic segment implies infinitely many periodic solutions"
Proceedings of the American Mathematical Society 135 no. 8 (2007), 2637-2647
(co-author Wacław Marzantowicz,)

"Discrete version of geometric method for detecting chaotic dynamics"
Topology and its Applications 152 (2005), 70-82
(co-author Marian Mrozek,)

"Topological horseshoes and delay differential equations"
Discrete and Continuous Dynamical Systems 12 no. 5 (2005), 827-852
(co-author Piotr Zgliczyński,)

"Isolating segments, fixed point index and symbolic dynamics III. Applications"
Journal of Differential Equations 183 (2002), 262-278
(co-author Piotr Zgliczyński,)

"Isolating segments, fixed point index and symbolic dynamics II. Homoclinic solutions"
Journal of Differential Equations 172 (2001), 189-211
(co-author Piotr Zgliczyński,)

"Isolating segments, fixed point index and symbolic dynamics"
Journal of Differential Equations 161 (2000), 245-288
(co-author Piotr Zgliczyński,)

"A geometric method for detecting chaotic dynamics"
Journal of Differential Equations 135 no. 1 (1997), 66-82
(co-author Roman Srzednicki, )





"A dictionary definition of chaos is a disordered state of collection; a confused mixture. This is an accurate description of dynamical systems theory today - or of any other lively field of research"

Morris W. Hirsch



CONLEY INDEX THEORY

"On the cohomology of an isolating block and its invariant part"
Topological Methods in Nonlinear Analysis vol. 32 no. 2 (2008), 313-326
(co-author Anna Gierzkiewicz, )

"Conley index and permanence in dynamical systems"
Topological Methods in Nonlinear Analysis 12 (1998), 153-158

"On the discrete Conley index in the invariant subspace"
Topology and its Applications 87 (1998), 105-116
(co-authors Piotr Zgliczyński and Andrzej Szymczak)



PERIODIC and HOMOCLINIC SOLUTIONS OF DIFFERENTIAL EQUATIONS

"Isolating segments for Caratheodory systems and existence of periodic solutions"
Proceedings of the American Mathematical Society 131 no. 8 (2002), 2443 -2451
(co-author Maciej Capiński)

"How to show an existence of homoclinic trajectories using topological tools"
Proceedeings Equadiff Berlin '99 World Scientific, Singapore, New Jersey, London, Hong-Kong
(co-author Piotr Zgliczyński,)

"Periodic segment and Nielsen numbers"
in "Conley Index Theory" 1999, Banach Center Publications 47, 247-252

"On detecting periodic solutions and chaos in the time periodically forced ODE's"
Nonlinear Analysis Theory, Methods and Applications 45 (2001), 19-27

"Isolating segments and anti-periodic solutions"
Monatshefte f. Mathematics 135 (2002), 245-252







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