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The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups
| Softcover ISBN: | 978-1-4704-7308-2 |
| Product Code: | MEMO/307/1552 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-8093-6 |
| Product Code: | MEMO/307/1552.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7308-2 |
| eBook: ISBN: | 978-1-4704-8093-6 |
| Product Code: | MEMO/307/1552.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups
| Softcover ISBN: | 978-1-4704-7308-2 |
| Product Code: | MEMO/307/1552 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-8093-6 |
| Product Code: | MEMO/307/1552.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7308-2 |
| eBook ISBN: | 978-1-4704-8093-6 |
| Product Code: | MEMO/307/1552.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 307; 2025; 192 ppMSC: Primary 37
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Table of Contents
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Chapters
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1. Introduction
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2. General Preliminaries on Rational Semigroups
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1. Ergodic Theory and Dynamics of Finitely Generated *Semi-Hyperbolic Rational Semigroups
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3. Basic Properties of Semi-hyperbolic and *Semi-Hyperbolic Rational Semigroups
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4. The Conformal and Invariant Measures $m_t$ and $\mu _t$ for $\tilde f:J(\tilde f)\longrightarrow J(\tilde f)$
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2. Ergodic Theory and Dynamics of Totally and Finely Non-Recurrent Rational Semigroups
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5. Totally Non-Recurrent and Finely Non-Recurrent Rational Semigroups
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6. Nice Sets (Families)
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7. The Behavior of the Absolutely Continuous Invariant Measures $\mu _t$ Near Critical Points
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8. Small Pressure $\mathrm {P}_V^\Xi (t)$
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9. Symbol Space Thermodynamic Formalism Associated to Nice Families: Real Analyticity of the Original Pressure $\mathrm {P}(t)$
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10. Invariant Measures: $\mu _t$ versus $\tilde \mu _t\circ \pi _\mathcal {U}^{-1}$; Finiteness of $\mu _t$
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11. Variational Principle: The Invariant Measures $\mu _t$ are the Unique Equilibrium States
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12. Decay of Correlations, Central Limit Theorems, the Law of Iterated Logarithm: The Method of Lai–Sang Young Towers
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3. Geometry of Finely Non-Recurrent Rational Semigroups Satisfying the Nice Open Set Condition
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13. Nice Open Set Condition (for any Rational Semigroup)
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14. Hausdorff Dimension of Invariant Measures $\mu _t$ and Multifractal Analysis of Lyapunov Exponents
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15. Measures $m_t\circ p_2^{-1}$ and $\mu _t\circ p_2^{-1}$ versus Hausdorff Measures $\mathrm {H}_{t^\kappa }$ and $\mathrm {H}_{t^\kappa \exp \left (c\sqrt {\log (1/t)\log ^3(1/t)}\right )}$
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16. $\operatorname {HD}(J(G))$ versus Hausdorff Dimension of Fiber Julia Sets $J_\omega $, $\omega \in \Sigma _u$
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17. Examples
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4. Appendices
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A. Absolutely Continuous $\sigma $-finite Invariant Measures: Martens Method
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B. Corrected Proofs of Lemma 7.9 and Lemma 7.10 from \cite{SUSH}
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C. Definitions of Classes of Rational Semigroups Used and Relations Between Them
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D. Open Problems
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
Volume: 307; 2025; 192 pp
MSC: Primary 37
-
Chapters
-
1. Introduction
-
2. General Preliminaries on Rational Semigroups
-
1. Ergodic Theory and Dynamics of Finitely Generated *Semi-Hyperbolic Rational Semigroups
-
3. Basic Properties of Semi-hyperbolic and *Semi-Hyperbolic Rational Semigroups
-
4. The Conformal and Invariant Measures $m_t$ and $\mu _t$ for $\tilde f:J(\tilde f)\longrightarrow J(\tilde f)$
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2. Ergodic Theory and Dynamics of Totally and Finely Non-Recurrent Rational Semigroups
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5. Totally Non-Recurrent and Finely Non-Recurrent Rational Semigroups
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6. Nice Sets (Families)
-
7. The Behavior of the Absolutely Continuous Invariant Measures $\mu _t$ Near Critical Points
-
8. Small Pressure $\mathrm {P}_V^\Xi (t)$
-
9. Symbol Space Thermodynamic Formalism Associated to Nice Families: Real Analyticity of the Original Pressure $\mathrm {P}(t)$
-
10. Invariant Measures: $\mu _t$ versus $\tilde \mu _t\circ \pi _\mathcal {U}^{-1}$; Finiteness of $\mu _t$
-
11. Variational Principle: The Invariant Measures $\mu _t$ are the Unique Equilibrium States
-
12. Decay of Correlations, Central Limit Theorems, the Law of Iterated Logarithm: The Method of Lai–Sang Young Towers
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3. Geometry of Finely Non-Recurrent Rational Semigroups Satisfying the Nice Open Set Condition
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13. Nice Open Set Condition (for any Rational Semigroup)
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14. Hausdorff Dimension of Invariant Measures $\mu _t$ and Multifractal Analysis of Lyapunov Exponents
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15. Measures $m_t\circ p_2^{-1}$ and $\mu _t\circ p_2^{-1}$ versus Hausdorff Measures $\mathrm {H}_{t^\kappa }$ and $\mathrm {H}_{t^\kappa \exp \left (c\sqrt {\log (1/t)\log ^3(1/t)}\right )}$
-
16. $\operatorname {HD}(J(G))$ versus Hausdorff Dimension of Fiber Julia Sets $J_\omega $, $\omega \in \Sigma _u$
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17. Examples
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4. Appendices
-
A. Absolutely Continuous $\sigma $-finite Invariant Measures: Martens Method
-
B. Corrected Proofs of Lemma 7.9 and Lemma 7.10 from \cite{SUSH}
-
C. Definitions of Classes of Rational Semigroups Used and Relations Between Them
-
D. Open Problems
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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