The conley index and non-existence of minimal homeomorphisms

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

A Minimal Non-solvable Group of Homeomorphisms

Let PL0(I) represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable groupW and show thatW embeds in every non-solvable subgroup of PL0(I). We find mild conditions under which other non-solvable subgroups (B, (≀Z≀), (Z≀), and (≀Z)) embed in subgroups of ...

Shift Equivalence and the Conley Index

In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Lastly, we define partially ordered Morse decom...

Construction and Properties of the Conley Index

The Existence of Periodic Travelling Waves for Singularly Perturbed Predator-Prey Equations via the Conley Index

This paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations, which arise as models of predator-prey interactions in mathematical ecology. The relevant equations are somewhat similar to the Fitz-Hugh-Nagumo equations, and our results apply to this latter system as well. In studying the Fitz-Hugh-Nagumo equations, Conley ([ 3 I), initiated a new...