The pruning front conjecture, folding patterns and classification of H\'enon maps in the presence of strange attractors

We study the topological dynamics of H\'enon maps. For a parameter set generalizing the Benedicks-Carleson parameters (the Wang-Young parameter set) we obtain the following: The pruning front conjecture (due to Cvitanovi\'c); A kneading theory (realizing a conjecture by Benedicks and Carleson); A classification: two H\'enon maps are conjugate on their strange attractors if and only if their sets of kneading sequences coincide, if and only if their folding patterns coincide. The folding pattern is a single sequence of 0s and 1s, which allows to distinguish two nonconjugate H\'enon attractors in finitely many steps. The classification result relies on further development of the authors' recent inverse limit description of H\'enon attractors in terms of densely branching trees.Comment: The case b < 0 is adde

Translation algorithms for graph covers

Graph covers are a way to describe continuous maps (and homeomorphisms) of the Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\ non-minimality or aperiodicty are no restrictions). We give a survey on the construction, properties and some special cases of graph covers

Od Antychrysta do sprzymierzeńca Goga – zmieniająca się rola islamu w interpretacjach premillenarystów

It was after the September 11, 2001 that Islam began to play a role in American Protestant visions of Armageddon. However, the Islam issue appeared in Protestant prophetic theology much earlier. Premilleniarians’ interpretations of the Holy Bible frequently concentrate on Islam and the Muslim world as an important factor of Armageddon.In the United States the Protestant concept of Armageddon was based in the 19ᵗʰ century in the theological stream of dispensationalism. According to this concept the identity of Antichrist was changed several times but it was the Islam world which influenced this identity most.Theories about Islam and Armageddon have been arising since the 7ᵗʰ century. Especially, during the Peasant Crusade the negative attitudes towards the Muslims were natural. Christian authorities started to identify Mahomet with Antichrist, the synonym of plagues and apocalyptic disaster. In the 11ᵗʰ century, for instance, it was the result of growing position of the Muslim world and the decline of Christianity and its culture in the Near East.Martin Luther in his Bile in 1534 tried to compare Turkey to GOG (from the Book of Ezekiel). This vision of Martin Luther was present till the 19ᵗʰ century, till the collapse of Ottoman Empire. Then it was Russia (communism) and their allies in the Near East: Egypt, Iran and Algeria which took the place of GOG. After 1979 and the revolution in Iran American Protestant thinkers focused on ayatollahs as precursors of the Antichrist. In his 1994 book Hal Lindsey tried to convince the readers that the Islamic Ayatollah constituted the greatest threat to Christianity. The origins of the conflict between Islam and Christianity are partly embedded in the Holy Bible (Book of Ezekiel, Book of Daniel, Book of Revelation). However, new modern prophetic visions, which describe the representative of Islam and a full complexity of religious issues are very often an oversimplification.It was after the September 11, 2001 that Islam began to play a role in American Protestant visions of Armageddon. However, the Islam issue appeared in Protestant prophetic theology much earlier. Premilleniarians’ interpretations of the Holy Bible frequently concentrate on Islam and the Muslim world as an important factor of Armageddon.In the United States the Protestant concept of Armageddon was based in the 19ᵗʰ century in the theological stream of dispensationalism. According to this concept the identity of Antichrist was changed several times but it was the Islam world which influenced this identity most.Theories about Islam and Armageddon have been arising since the 7ᵗʰ century. Especially, during the Peasant Crusade the negative attitudes towards the Muslims were natural. Christian authorities started to identify Mahomet with Antichrist, the synonym of plagues and apocalyptic disaster. In the 11ᵗʰ century, for instance, it was the result of growing position of the Muslim world and the decline of Christianity and its culture in the Near East.Martin Luther in his Bile in 1534 tried to compare Turkey to GOG (from the Book of Ezekiel). This vision of Martin Luther was present till the 19ᵗʰ century, till the collapse of Ottoman Empire. Then it was Russia (communism) and their allies in the Near East: Egypt, Iran and Algeria which took the place of GOG. After 1979 and the revolution in Iran American Protestant thinkers focused on ayatollahs as precursors of the Antichrist. In his 1994 book Hal Lindsey tried to convince the readers that the Islamic Ayatollah constituted the greatest threat to Christianity. The origins of the conflict between Islam and Christianity are partly embedded in the Holy Bible (Book of Ezekiel, Book of Daniel, Book of Revelation). However, new modern prophetic visions, which describe the representative of Islam and a full complexity of religious issues are very often an oversimplification