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Dynamical systems / [edited by] Araceli Bonifant.

By: Contributor(s): Material type: TextTextSeries: Collected papers of John Milnor ; VI, VII.Publication details: Providence : American Mathematical Society, 2012. (VI) 2014. (VII)Description: xii, 546 p. : illustrations ; 26 cm; xvi, 592 p. : illustrations (some color) ; 26 cmISBN:
  • 9780821891391 (vi)
  • 9781470409371 (vii)
Subject(s): DDC classification:
  • 515.39 23 M659
Contents:
VI: pt. I REAL DYNAMICS -- Introduction -- The characteristics of a vector field on the two-sphere (1953) -- On the concept of attractor (1985) -- On the concept of attractor: correction and remarks (1985) -- Directional entropies of cellular automaton-maps (1986) -- On the entropy geometry of cellular automata (1988) -- Non-expansive Henon maps (1988) -- On iterated maps of the interval (1988) / W. Thurston -- A monotonicity conjecture for real cubic maps (1995) / C. Tresser -- On entropy and monotonicity for real cubic maps (2000) / P. Sentenac -- Fubini foiled: Katok's paradoxical example in measure theory (1997) -- pt. II COMPLEX DYNAMICS -- Introduction -- Dynamical properties of plane polynomial automorphisms (1989) / S. Friedland -- Self-similarity and hairiness in the Mandelbrot set (1989) -- Remarks on iterated cubic maps (1992) -- Geometry and dynamics of quadratic rational maps (1993) / Tan Lei -- The Fibonacci unimodal map (1993) / M. Lyubich -- Fixed points of polynomial maps. Part II: Fixed point portraits (1993) / L. Goldberg -- The mathematical work of Curt McMullen (1999).
VII: Preface -- Dedication -- Acknowledgments -- Addendum: updated references -- Introduction -- Notes on surjective cellular automaton-maps (unpublished manuscript of 1984) -- Tsujii's monotonicity proof for real quadratic maps (unpublished manuscript of 2000) -- Local connectivity of Julia sets: expository lectures (2000) -- On rational maps with two critical points (2000) -- Periodic orbits, external rays and the Mandelbrot set: an expository account (2000) -- Pasting together Julia sets - a worked out example of mating (2004) -- On Lattès maps (2006) -- Elliptic curves as attractors in P², Part I: dynamics (2007) / with A. Bonifant and M. Dabija --Schwarzian derivatives and cylinder maps (2008) / with A. Bonifant -- Cubic polynomial maps with periodic critical orbit, Part I (2009) -- Cubic polynomial maps with periodic critical orbit, Part II: escape regions (2010) / with A. Bonifant and J. Kiwi -- Errata for "Cubic polynomial maps with periodic critical orbit, Part II: escape regions (2010)" / with A. Bonifant and J. Kiwi -- Hyperbolic components (2012) / with an appendix by A. Poirier.
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VI: 1953-2000
VII: 1984-2012

Includes bibliographical references and indexes.

VI:
pt. I REAL DYNAMICS --
Introduction --
The characteristics of a vector field on the two-sphere (1953) --
On the concept of attractor (1985) --
On the concept of attractor: correction and remarks (1985) --
Directional entropies of cellular automaton-maps (1986) --
On the entropy geometry of cellular automata (1988) --
Non-expansive Henon maps (1988) --
On iterated maps of the interval (1988) / W. Thurston --
A monotonicity conjecture for real cubic maps (1995) / C. Tresser --
On entropy and monotonicity for real cubic maps (2000) / P. Sentenac --
Fubini foiled: Katok's paradoxical example in measure theory (1997) --
pt. II COMPLEX DYNAMICS --
Introduction --
Dynamical properties of plane polynomial automorphisms (1989) / S. Friedland --
Self-similarity and hairiness in the Mandelbrot set (1989) --
Remarks on iterated cubic maps (1992) --
Geometry and dynamics of quadratic rational maps (1993) / Tan Lei --
The Fibonacci unimodal map (1993) / M. Lyubich --
Fixed points of polynomial maps. Part II: Fixed point portraits (1993) / L. Goldberg --
The mathematical work of Curt McMullen (1999).

VII:
Preface --
Dedication --
Acknowledgments --
Addendum: updated references --
Introduction --
Notes on surjective cellular automaton-maps (unpublished manuscript of 1984) --
Tsujii's monotonicity proof for real quadratic maps (unpublished manuscript of 2000) --
Local connectivity of Julia sets: expository lectures (2000) --
On rational maps with two critical points (2000) --
Periodic orbits, external rays and the Mandelbrot set: an expository account (2000) --
Pasting together Julia sets - a worked out example of mating (2004) --
On Lattès maps (2006) --
Elliptic curves as attractors in P², Part I: dynamics (2007) / with A. Bonifant and M. Dabija --Schwarzian derivatives and cylinder maps (2008) / with A. Bonifant --
Cubic polynomial maps with periodic critical orbit, Part I (2009) --
Cubic polynomial maps with periodic critical orbit, Part II: escape regions (2010) / with A. Bonifant and J. Kiwi --
Errata for "Cubic polynomial maps with periodic critical orbit, Part II: escape regions (2010)" / with A. Bonifant and J. Kiwi --
Hyperbolic components (2012) / with an appendix by A. Poirier.

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